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Extremal results for Berge-hypergraphsMay 29 2015Let $G$ be a graph and $\mathcal{H}$ be a hypergraph both on the same vertex set. We say that a hypergraph $\mathcal{H}$ is a \emph{Berge}-$G$ if there is a bijection $f : E(G) \rightarrow E(\mathcal{H})$ such that for $e \in E(G)$ we have $e \subset ... More

On Berge-Ramsey problemsJun 06 2019Given a graph $G$, a hypergraph $\mathcal{H}$ is a Berge copy of $F$ if $V(G)\subset V(\mathcal{H})$ and there is a bijection $f:E(G)\rightarrow E(\mathcal{H})$ such that for any edge $e$ of $G$ we have $e\subset f(e)$. We study Ramsey problems for Berge ... More

The covering lemma and $q$-analogues of extremal set theory problemsMay 16 2019May 28 2019We prove a general lemma (inspired by a lemma of Holroyd and Talbot) about the connection of the largest cardinalities (or weight) of structures satisfying some hereditary property and substructures satisfying the same hereditary property. We use it to ... More

The covering lemma and $q$-analogues of extremal set theory problemsMay 16 2019We prove a general lemma (inspired by a lemma of Holroyd and Talbot) about the connection of the largest cardinalities (or weight) of structures satisfying some hereditary property and substructures satisfying the same hereditary property. We use it to ... More

A note on the Turán number of a Berge odd cycleMar 03 2019In this note we obtain upper bounds on the number of hyperedges in 3-uniform hypergraphs not containing a Berge cycle of given odd length. We improve the bound given by F\"uredi and \"Ozkahya. The result follows from a more general theorem. We also obtain ... More

Between the deterministic and non-deterministic query complexityJul 22 2019We consider problems that can be solved by asking certain queries. The deterministic query complexity $D(P)$ of a problem $P$ is the smallest number of queries needed to ask in order to find the solution (in the worst case), while the non-deterministic ... More

Majority problems of large query sizeOct 28 2016The aim of this paper is twofold: we present improvements of results of De Marco and Kranakis [6] on majority models, and we also survey recent results concerning the generalizations of the pairing model with query size k, and also provide bounds on their ... More

Path-search in the pyramid and in other graphsApr 27 2011We are given an acyclic directed graph with one source, and a subset of its edges which contains exactly one outgoing edge for every non-sink vertex. These edges determine a unique path from the source to a sink. We can think of it as a switch in every ... More

Rounds in a combinatorial search problemNov 30 2016We consider the following combinatorial search problem: we are given some excellent elements of $[n]$ and we should find at least one, asking questions of the following type: "Is there an excellent element in $A \subset [n]$?". G.O.H. Katona proved sharp ... More

Hypergraphs without exponentsJun 16 2019Here we give a short, concise proof for the following result. There exists a $k$-uniform hypergraph $H$ (for $k\geq 5$) without exponent, i.e., when the Tur\'an function is not polynomial in $n$. More precisely, we have $ex(n,H)=o(n^{k-1})$ but it exceeds ... More

Edge-decomposition of graphs into copies of a tree with four edgesMar 08 2012We study edge-decompositions of highly connected graphs into copies of a given tree. In particular we attack the following conjecture by Bar\'at and Thomassen: for each tree $T$, there exists a natural number $k_T$ such that if $G$ is a $k_T$-edge-connected ... More

A plurality problem with three colors and query size threeAug 19 2017The Plurality problem - introduced by Aigner \cite{A2004} - has many variants. In this article we deal with the following version: suppose we are given $n$ balls, each of them colored by one of three colors. A \textit{plurality ball} is one such that ... More

Generalizations of the Tree Packing ConjectureApr 04 2011Oct 21 2011The Gy\'arf\'as tree packing conjecture asserts that any set of trees with $2,3, ..., k$ vertices has an (edge-disjoint) packing into the complete graph on $k$ vertices. Gy\'arf\'as and Lehel proved that the conjecture holds in some special cases. We ... More

Finding non-minority balls with majority and plurality queriesDec 20 2018Given a set of $n$ colored balls, a \textit{majority, non-minority or plurality ball} is one whose color class has size more than $n/2$, at least $n/2$ or larger than any other color class, respectively. We describe linear time algorithms for finding ... More

A discrete isodiametric result: the Erdős-Ko-Rado theorem for multisetsDec 05 2012Mar 09 2014There are many generalizations of the Erd\H{o}s-Ko-Rado theorem. We give new results (and problems) concerning families of $t$-intersecting $k$-element multisets of an $n$-set and point out connections to coding theory and classical geometry. We establish ... More

Stability results on vertex Turán problems in Kneser graphsApr 11 2018Apr 20 2018The vertex set of the Kneser graph $K(n,k)$ is $V = \binom{[n]}{k}$ and two vertices are adjacent if the corresponding sets are disjoint. For any graph $F$, the largest size of a vertex set $U \subseteq V$ such that $K(n,k)[U]$ is $F$-free, was recently ... More

On the maximum number of copies of H in graphs with given size and orderOct 01 2018We study the maximum number $ex(n,e,H)$ of copies of a graph $H$ in graphs with given number of vertices and edges. We show that for any fixed graph $H$, $ex(n,e,H)$ is asymptotically realized by the quasi-clique provided that the edge density is sufficiently ... More

Stability results on vertex Turán problems in Kneser graphsApr 11 2018Mar 07 2019The vertex set of the Kneser graph $K(n,k)$ is $V = \binom{[n]}{k}$ and two vertices are adjacent if the corresponding sets are disjoint. For any graph $F$, the largest size of a vertex set $U \subseteq V$ such that $K(n,k)[U]$ is $F$-free, was recently ... More

t-wise Berge and t-heavy hypergraphsFeb 08 2019In many proofs concerning extremal parameters of Berge hypergraphs one starts with analyzing that part of that shadow graph which is contained in many hyperedges. Capturing this phenomenon we introduce two new types of hypergraphs. A hypergraph $\mathcal{H}$ ... More

Advantage in the discrete Voronoi gameMar 03 2013We study the discrete Voronoi game, where two players alternately claim vertices of a graph for t rounds. In the end, the remaining vertices are divided such that each player receives the vertices that are closer to his or her claimed vertices. We prove ... More

Topological orderings of weighted directed acyclic graphsOct 01 2013Sep 19 2016We call a topological ordering of a weighted directed acyclic graph non-negative if the sum of weights on the vertices in any prefix of the ordering is non-negative. We investigate two processes for constructing non-negative topological orderings of weighted ... More

Search for the end of a path in the d-dimensional grid and in other graphsNov 13 2012Sep 01 2016We consider the worst-case query complexity of some variants of certain \cl{PPAD}-complete search problems. Suppose we are given a graph $G$ and a vertex $s \in V(G)$. We denote the directed graph obtained from $G$ by directing all edges in both directions ... More

On the number of cycles in a graph with restricted cycle lengthsOct 11 2016Let $L$ be a set of positive integers. We call a (directed) graph $G$ an $L$\emph{-cycle graph} if all cycle lengths in $G$ belong to $L$. Let $c(L,n)$ be the maximum number of cycles possible in an $n$-vertex $L$-cycle graph (we use $\vec{c}(L,n)$ for ... More

On Clique Coverings of Complete Multipartite GraphsSep 05 2018A clique covering of a graph $G$ is a set of cliques of $G$ such that any edge of $G$ is contained in one of these cliques, and the weight of a clique covering is the sum of the sizes of the cliques in it. The sigma clique cover number $scc(G)$ of a graph ... More

Line Percolation in Finite Projective PlanesAug 01 2016We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal non-percolating sets. Additional results on the ... More

On the weight of Berge-$F$-free hypergraphsFeb 09 2019For a graph $F$, we say a hypergraph is a Berge-$F$ if it can be obtained from $F$ by replacing each edge of $F$ with a hyperedge containing it. A hypergraph is Berge-$F$-free if it does not contain a subhypergraph that is a Berge-$F$. The weight of a ... More

Linearity of Saturation for Berge HypergraphsJul 18 2018For a graph $F$, we say a hypergraph $H$ is Berge-$F$ if it can be obtained from $F$ be replacing each edge of $F$ with a hyperedge containing it. We say a hypergraph is Berge-$F$-saturated if it does not contain a Berge-$F$, but adding any hyperedge ... More

Density-based group testingApr 06 2012In this paper we study a new, generalized version of the well-known group testing problem. In the classical model of group testing we are given n objects, some of which are considered to be defective. We can test certain subsets of the objects whether ... More

Ramsey problems for Berge hypergraphsAug 30 2018Dec 17 2018For a graph $G$, a hypergraph $\mathcal{H}$ is a Berge copy of $G$ (or a Berge-$G$ in short), if there is a bijection $f : E(G) \rightarrow E(\mathcal{H})$ such that for each $e \in E(G)$ we have $e \subset f(e)$. We denote the family of $r$-uniform hypergraphs ... More

On the weight of Berge-$F$-free hypergraphsFeb 09 2019Mar 13 2019For a graph $F$, we say a hypergraph is a Berge-$F$ if it can be obtained from $F$ by replacing each edge of $F$ with a hyperedge containing it. A hypergraph is Berge-$F$-free if it does not contain a subhypergraph that is a Berge-$F$. The weight of a ... More

Cross-Sperner familiesApr 20 2011A pair of families $(\cF,\cG)$ is said to be \emph{cross-Sperner} if there exists no pair of sets $F \in \cF, G \in \cG$ with $F \subseteq G$ or $G \subseteq F$. There are two ways to measure the size of the pair $(\cF,\cG)$: with the sum $|\cF|+|\cG|$ ... More

An improvement on the maximum number of $k$-Dominating Independent SetsSep 14 2017Erd\H{o}s and Moser raised the question of determining the maximum number of maximal cliques or equivalently, the maximum number of maximal independent sets in a graph on $n$ vertices. Since then there has been a lot of research along these lines. A $k$-dominating ... More

Majority and Plurality ProblemsMar 07 2012Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class; respectively. ... More

Forbidding rank-preserving copies of a posetOct 25 2017The maximum size, $La(n,P)$, of a family of subsets of $[n]=\{1,2,...,n\}$ without containing a copy of $P$ as a subposet, has been intensively studied. Let $P$ be a graded poset. We say that a family $\mathcal{F}$ of subsets of $[n]=\{1,2,...,n\}$ contains ... More

Rainbow Ramsey problems for the Boolean latticeSep 23 2018We address the following rainbow Ramsey problem: For posets $P,Q$ what is the smallest number $n$ such that any coloring of the elements of the Boolean lattice $B_n$ either admits a monochromatic copy of $P$ or a rainbow copy of $Q$. We consider both ... More

On the number of containments in $P$-free familiesApr 04 2018A subfamily $\{F_1,F_2,\dots,F_{|P|}\}\subseteq \mathcal F$ is a copy of the poset $P$ if there exists a bijection $i:P\rightarrow \{F_1,F_2,\dots,F_{|P|}\}$ such that $p\le_P q$ implies $i(p)\subseteq i(q)$. A family $\mathcal F$ is $P$-free, if it does ... More

Vertex Turán problems for the oriented hypercubeJul 18 2018In this short note we consider the oriented vertex Tur\'an problem in the hypercube: for a fixed oriented graph $\overrightarrow{F}$, determine the maximum size $ex_v(\overrightarrow{F}, \overrightarrow{Q_n})$ of a subset $U$ of the vertices of the oriented ... More

Maps on quantum states preserving Bregman and Jensen divergencesJan 25 2016Jul 01 2016We describe the structure of the bijective transformations on the set of density operators which preserve the Bregman $f$-divergence for an arbitrary differentiable strictly convex function $f.$ Furthermore, we determine the preservers of the Jensen $f$-divergence ... More

Jointly convex quantum Jensen divergencesDec 14 2017Mar 08 2018We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which ... More

On a problem of Bauschke and BorweinDec 05 2014Aug 03 2015Consider a differentiable convex function $f: \mathbb{R}^n \supset \mathrm{dom} f \rightarrow \mathbb{R}.$ The induced spectral function $F$ is given by $F=f \circ \lambda,$ where $\lambda: \mathbf{M}_n^{sa} \rightarrow \mathbb{R}^{n}$ is the eigenvalue ... More

PHENIX results on Lévy analysis of Bose-Einstein correlation functionsOct 17 2016The nature of the quark-hadron phase transition can be investigated through analyzing the space-time structure of the hadron emission source. For this, the Bose-Einstein or HBT correlations of identified charged particles are among the best observables. ... More

Tractable hypergraph properties for constraint satisfaction and conjunctive queriesNov 04 2009Dec 06 2011An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP instances (i.e., where ... More

Characterizations of centrality by local convexity of certain functions on $C^*$-algebrasSep 11 2017Feb 15 2018We provide a function class which is useful to distinguish central and non-central elements of a $C^*$-algebra in the following sense: for each element $f$ of this function class, a self-adjoint element $a$ of a $C^*$-algebra is central if and only if ... More

Quantum $f$-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spacesFeb 22 2016Mar 18 2016We determine the structure of all bijections on the cone of positive semidefinite operators which preserve the quantum $f$-divergence for an arbitrary strictly convex function $f$ defined on the positive halfline. It turns out that any such transformation ... More

50+ Metrics for Calendar MiningJan 01 2016In this report we propose 50+ metrics which can be measured by organizations in order to identify improvements in various areas such as meeting efficiency, capacity planning or leadership skills, just to new a few. The notion of calendar mining is introduced ... More

A class of characterizations of central elements in $C^*$-algebrasAug 18 2016Let $\mathcal{A}$ be a unital $C^*$-algebra. We introduce a quite large function class $\mathcal{F}$ (which includes the power function $x \mapsto x^p$ for any $p \in (1, \infty)$), and show that any function $f \in \mathcal{F}$ provides a characterization ... More

An overview of radial pulsations of relativistic stellar models for dissipative fluidsApr 01 2019In this paper we present a review of radial oscillations of neutron stars which complements earlier studies. We consider oscillations that are damped by the presence of viscosity and thermal conductivity in the nuclear matter which directly determine ... More

Connections between centrality and local monotonicity of certain functions on $C^*$-algebrasAug 18 2016Apr 12 2017We introduce a quite large class of functions (including the exponential function and the power functions with exponent greater than one), and show that for any element $f$ of this function class, a self-adjoint element $a$ of a $C^*$-algebra is central ... More

Maps on probability measures preserving certain distances --- a survey and some new resultsFeb 09 2018Mar 19 2018Borel probability measures living on metric spaces are fundamental mathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in ... More

PHENIX results on Bose-Einstein correlation functionsFeb 15 2016Measurement of Bose-Einstein or HBT correlations of identified charged particles provide insight into the space-time structure of particle emitting sources in heavy-ion collisions. In this paper we present the latest results from the RHIC PHENIX experiment ... More

Applications of an intersection formula to dual conesApr 03 2017Oct 19 2017We give a succinct proof of a duality theorem obtained by R\'ev\'esz in 1991 which concerns extremal quantities related to trigonomertic polynomials. The key tool of our new proof is an intersection formula on dual cones in real Banach spaces. We show ... More

Fundamental oscillation modes and thermal relaxation in young neutron starsAug 07 2019We present a novel survey of the radial oscillation modes and relaxation of neutron stars for various types of nuclear-theory-based EOS of cold neutron-star matter. This study complements our earlier qualitative study of the effect of viscosity and thermal ... More

Complete intersection quiver settings with one dimensional verticesMay 16 2011Jul 17 2011We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction ... More

Saturating Sperner familiesMay 23 2011A family $\cF \subseteq 2^{[n]}$ saturates the monotone decreasing property $\cP$ if $\cF$ satisfies $\cP$ and one cannot add any set to $\cF$ such that property $\cP$ is still satisfied by the resulting family. We address the problem of finding the minimum ... More

Generalising separating families of fixed sizeSep 01 2015We examine the following version of a classic combinatorial search problem introduced by R\'enyi: Given a finite set $X$ of $n$ elements we want to identify an unknown subset $Y \subset X$ of exactly $d$ elements by testing, by as few as possible subsets ... More

Finding a non-minority ball with majority answersSep 28 2015Sep 28 2016Suppose we are given a set of $n$ balls $\{b_1,\ldots,b_n\}$ each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls $\{b_{i_1},b_{i_2},b_{i_3}\}$. As an answer to such ... More

Two-part set systemsOct 01 2011The two part Sperner theorem of Katona and Kleitman states that if $X$ is an $n$-element set with partition $X_1 \cup X_2$, and $\cF$ is a family of subsets of $X$ such that no two sets $A, B \in \cF$ satisfy $A \subset B$ (or $B \subset A$) and $A \cap ... More

Adaptive Majority Problems for Restricted Query Graphs and for Weighted SetsMar 20 2019Suppose that the vertices of a graph $G$ are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study ... More

Peeling and Nibbling the Cactus: Subexponential-Time Algorithms for Counting Triangulations and Related ProblemsMar 23 2016Given a set of $n$ points $S$ in the plane, a triangulation $T$ of $S$ is a maximal set of non-crossing segments with endpoints in $S$. We present an algorithm that computes the number of triangulations on a given set of $n$ points in time $n^{(11+ o(1))\sqrt{n} ... More

On algebraic endomorphisms of the Einstein gyrogroupJun 20 2015We describe the structure of all continuous algebraic endomorphisms of the open unit ball $\mathbf{B}$ of $\mathbb{R}^3$ equipped with the Einstein velocity addition. We show that any nonzero such transformation originates from an orthogonal linear transformation ... More

A characterization theorem for matrix variancesNov 15 2013Jul 01 2014Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of observables ... More

On the hardness of losing weightNov 10 2017We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a better (lighter, ... More

Uncountable strongly surjective linear ordersJun 30 2017Jan 30 2018A linear order $L$ is strongly surjective if $L$ can be mapped onto any of its suborders in an order preserving way. We prove various results on the existence and non-existence of uncountable strongly surjective linear orders answering questions of Camerlo, ... More

Trees, ladders and graphsSep 09 2014We introduce a new method to construct uncountably chromatic graphs from non special trees and ladder systems. Answering a question of P. Erd\H{o}s and A. Hajnal from 1985, we construct graphs of chromatic number $\omega_1$ without uncountable $\omega$-connected ... More

Continuous Jordan triple endomorphisms of $\mathbb{P}_2$Jun 20 2015We describe the structure of all continuous Jordan triple endomorphisms of the set $\mathbb{P}_2$ of all positive definite $2\times 2$ matrices thus completing a recent result of ours. We also mention an application concerning sorts of surjective generalized ... More

Fundamental Analysis of a Developer Support Chat Log for Identifying Process Improvement OpportunitiesMar 18 2015In this report analysis of a support chat log of a development team is shown. Developer support chat is used to provide internal support to other development teams. The report shows how a fundamental data analysis helped to identify gaps and action items ... More

Random walk hierarchy measure: What is more hierarchical, a chain, a tree or a star?Aug 31 2015Signs of hierarchy are prevalent in a wide range of systems in nature and society. One of the key problems is quantifying the importance of hierarchical organisation in the structure of the network representing the interactions or connections between ... More

An exact characterization of tractable demand patterns for maximum disjoint path problemsNov 04 2014We study the following general disjoint paths problem: given a supply graph $G$, a set $T\subseteq V(G)$ of terminals, a demand graph $H$ on the vertices $T$, and an integer $k$, the task is to find a set of $k$ pairwise vertex-disjoint valid paths, where ... More

Fixed-parameter tractability of multicut parameterized by the size of the cutsetOct 18 2010Sep 03 2013Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the ... More

Orientations of graphs with uncountable chromatic numberAug 24 2016A graph (digraph) has uncountable chromatic number if its vertices cannot be covered by countably many independent (acyclic) sets. Our aim is to investigate digraphs with uncountable chromatic number and orientations of undirected graphs with uncountable ... More

Toric quiver cellsSep 12 2016It is shown that up to dimension four, the toric ideal of a quiver polytope is generated in degree two, with the only exception of the four-dimensional Birkhoff polytope. As a consequence, B{\o}gvad's conjecture holds for quiver polytopes of dimension ... More

Painlevé test of coupled Gross-Pitaevskii equationsSep 21 2003Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried out with the result that the coupled equations pass the P-test only if a special relation containing system parameters (masses, scattering lengths) is satisfied. Computer algebra ... More

Kernelization of Packing ProblemsDec 07 2018Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size at least k ... More

Prime congruences of idempotent semirings and a Nullstellensatz for tropical polynomialsAug 17 2014Sep 13 2017A new definition of prime congruences in additively idempotent semirings is given using twisted products. This class turns out to exhibit some analogous properties to the prime ideals of commutative rings. In order to establish a good notion of radical ... More

Density of 4-edge paths in graphs with fixed edge densityJan 06 2016We investigate the number of 4-edge paths in graphs with a fixed number of vertices and edges. An asymptotically sharp upper bound is given to this quantity. The extremal construction is the quasi-star or the quasi-clique graph, depending on the edge ... More

Ladder system uniformization on trees I & IIJun 11 2018Jan 04 2019Given a tree $T$ of height $\omega_1$, we say that a ladder system colouring $(f_\alpha)_{\alpha\in \lim\omega_1}$ has a $T$-uniformization if there is a function $\varphi$ defined on a subtree $S$ of $T$ so that for any $s\in S_\alpha$ of limit height ... More

Chordal Editing is Fixed-Parameter TractableMay 30 2014Graph modification problems are typically asked as follows: is there a small set of operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; ... More

Toric quiver cellsSep 12 2016Jul 03 2017It is shown that up to dimension four, the toric ideal of a quiver polytope is generated in degree two, with the only exception of the four-dimensional Birkhoff polytope. As a consequence, B{\o}gvad's conjecture holds for quiver polytopes of dimension ... More

Cleaning Interval GraphsMar 05 2010We investigate a special case of the Induced Subgraph Isomorphism problem, where both input graphs are interval graphs. We show the NP-hardness of this problem, and we prove fixed-parameter tractability of the problem with non-standard parameterization, ... More

Structure Theorem and Isomorphism Test for Graphs with Excluded Topological SubgraphsNov 04 2011Nov 13 2014We generalize the structure theorem of Robertson and Seymour for graphs excluding a fixed graph $H$ as a minor to graphs excluding $H$ as a topological subgraph. We prove that for a fixed $H$, every graph excluding $H$ as a topological subgraph has a ... More

Obtaining a Planar Graph by Vertex DeletionDec 29 2008In the k-Apex problem the task is to find at most k vertices whose deletion makes the given graph planar. The graphs for which there exists a solution form a minor closed class of graphs, hence by the deep results of Robertson and Seymour, there is an ... More

Some inequalities for quantum Tsallis entropy related to the strong subadditivityMar 27 2014Apr 23 2015In this paper we investigate the inequality $S_q(\rho_{123})+S_q(\rho_2)\leq S_q(\rho_{12})+S_q(\rho_{23}) \, (*)$ where $\rho_{123}$ is a state on a finite dimensional Hilbert space $\mathcal{H}_1\otimes \mathcal{H}_2\otimes \mathcal{H}_3,$ and $S_q$ ... More

Two infinite quantities and their surprising relationshipMar 12 2018As early as the 17th century, Galileo Galilei wondered how to compare the sizes of infinite sets. Fast forward almost four hundred years, and in the summer of 2017, at the 6th European Set Theory Conference, a young model theorist, Maryanthe Malliaris, ... More

On the dimension of polynomial semiringsOct 08 2015In our previous work, motivated by the study of tropical polynomials, a definition for prime congruences was given for an arbitrary commutative semiring. It was shown that for additively idempotent semirings this class exhibits some analogous properties ... More

The Collins-Roscoe mechanism and D-spacesOct 18 2010We prove that if a space X is well ordered $(\alpha A)$, or linearly semi-stratifiable, or elastic then X is a D-space.

Quantum Hellinger distances revisitedMar 25 2019May 10 2019This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. [Lett. Math. Phys. (2019), in press, arXiv:1901.01378] with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger ... More

On the equations and classification of toric quiver varietiesFeb 20 2014Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a quiver with ... More

A model with Suslin trees but no minimal uncountable linear orders other than $ω_1$ and $-ω_1$Mar 09 2018Mar 12 2018We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\omega_1$ and $-\omega_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration, proving that ... More

Prime congruences of idempotent semirings and a Nullstellensatz for tropical polynomialsAug 17 2014Sep 01 2015A new definition of prime congruences in additively idempotent semirings is given using twisted products. This class turns out to exhibit some analogous properties to the prime ideals of commutative rings. In order to establish a good notion of radical ... More

Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask)Jul 08 2013Aug 25 2013Given two graphs $H$ and $G$, the Subgraph Isomorphism problem asks if $H$ is isomorphic to a subgraph of $G$. While NP-hard in general, algorithms exist for various parameterized versions of the problem: for example, the problem can be solved (1) in ... More

Optimal parameterized algorithms for planar facility location problems using Voronoi diagramsApr 21 2015We study a general family of facility location problems defined on planar graphs and on the 2-dimensional plane. In these problems, a subset of $k$ objects has to be selected, satisfying certain packing (disjointness) and covering constraints. Our main ... More

The limited blessing of low dimensionality: when $1-1/d$ is the best possible exponent for $d$-dimensional geometric problemsDec 04 2016We are studying $d$-dimensional geometric problems that have algorithms with $1-1/d$ appearing in the exponent of the running time, for example, in the form of $2^{n^{1-1/d}}$ or $n^{k^{1-1/d}}$. This means that these algorithms perform somewhat better ... More

Subexponential parameterized algorithms for graphs of polynomial growthOct 25 2016We show that for a number of parameterized problems for which only $2^{O(k)} n^{O(1)}$ time algorithms are known on general graphs, subexponential parameterized algorithms with running time $2^{O(k^{1-\frac{1}{1+\delta}} \log^2 k)} n^{O(1)}$ are possible ... More

Quantum Hellinger distances revisitedMar 25 2019Apr 19 2019This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. [Lett. Math. Phys. (2019), in press, arXiv:1901.01378] with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger ... More

Probabilistic Constraints on the Mass and Composition of Proxima bFeb 08 2017Recent studies regarding the habitability, observability, and possible orbital evolution of the indirectly detected exoplanet Proxima b have mostly assumed a planet with $M \sim 1.3$ $M_\oplus$, a rocky composition, and an Earth-like atmosphere or none ... More

Triangle-different Hamiltonian pathsAug 18 2016Oct 11 2016Let $G$ be a fixed graph. Two paths of length $n-1$ on $n$ vertices (Hamiltonian paths) are $G$-different if there is a subgraph isomorphic to $G$ in their union. In this paper we prove that the maximal number of pairwise triangle-different Hamiltonian ... More

Complexity of counting subgraphs: only the boundedness of the vertex-cover number countsJul 10 2014For a class $\mathcal{H}$ of graphs, #Sub$(\mathcal{H})$ is the counting problem that, given a graph $H\in \mathcal{H}$ and an arbitrary graph $G$, asks for the number of subgraphs of $G$ isomorphic to $H$. It is known that if $\mathcal{H}$ has bounded ... More

A faster FPT algorithm for Bipartite ContractionMay 13 2013Sep 04 2013The \textsc{Bipartite Contraction} problem is to decide, given a graph $G$ and a parameter $k$, whether we can can obtain a bipartite graph from $G$ by at most $k$ edge contractions. The fixed-parameter tractability of the problem was shown by [Heggernes ... More

Saturation in random graphsOct 30 2015Apr 13 2016A graph $H$ is $K_s$-saturated if it is a maximal $K_s$-free graph, i.e., $H$ contains no clique on $s$ vertices, but the addition of any missing edge creates one. The minimum number of edges in a $K_s$-saturated graph was determined over 50 years ago ... More

Domination in 3-tournamentsFeb 04 2016A 3-tournament is a complete 3-uniform hypergraph where each edge has a special vertex designated as its tail. A vertex set $X$ dominates $T$ if every vertex not in $X$ is contained in an edge whose tail is in $X$. The domination number of $T$ is the ... More