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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Separating families of convex setsNov 13 2012Two elements, $x$ and $y$, are separated by a set $S$ if it contains exactly one of $x$ and $y$. We prove that any set of $n$ points in general position in the plane can be separated by $O(n\log\log n/\log n)$ convex sets, and for some point sets $\Omega(n/\log ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

Finding small patterns in permutations in linear timeJul 11 2013Oct 31 2013Given two permutations $\sigma$ and $\pi$, the \textsc{Permutation Pattern} problem asks if $\sigma$ is a subpattern of $\pi$. We show that the problem can be solved in time $2^{O(\ell^2\log \ell)}\cdot n$, where $\ell=|\sigma|$ and $n=|\pi|$. In other ... More

On the joint convexity of the Bregman divergence of matricesMay 30 2014Apr 23 2015We characterize the functions for which the corresponding Bregman divergence is jointly convex on matrices. As an application of this characterization, we derive a sharp inequality for the quantum Tsallis entropy of a tripartite state, which can be considered ... More

Orientations of graphs with uncountable chromatic numberAug 24 2016Nov 09 2017Motivated by an old conjecture of P. Erd\H{o}s and V. Neumann-Lara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountable chromatic number ... More

Improved Ramsey-type results in comparability graphsOct 01 2018Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if $G$ is an $n$-vertex graph ... 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

Interval Deletion is Fixed-Parameter TractableNov 26 2012May 06 2014We study the minimum \emph{interval deletion} problem, which asks for the removal of a set of at most $k$ vertices to make a graph of $n$ vertices into an interval graph. We present a parameterized algorithm of runtime $10^k \cdot n^{O(1)}$ for this problem, ... 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

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

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

Forbidden subposet problems with size restrictionsAug 23 2016Upper bounds to the size of a family of subsets of an n-element set that avoids certain configurations are proved. These forbidden configurations can be described by inclusion patterns and some sets having the same size. Our results are closely related ... 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

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

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

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

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

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

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

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

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

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

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

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

Covering Paths for Planar Point SetsMar 01 2013Given $n$ points in the plane, a \emph{covering path} is a polygonal path that visits all the points. If no three points are collinear, every covering path requires at least $n/2$ segments, and $n-1$ straight line segments obviously suffice even if the ... More

Global Controllability of Chemical ReactionsAug 13 2015Controllability of chemical reactions is an important problem in chemical engineering science. In control theory, analysis of the controllability of linear systems is well-founded, however the dynamics of chemical reactions is usually nonlinear. Global ... More

Mapping Directly Imaged Giant ExoplanetsOct 25 2012With the increasing number of directly imaged giant exoplanets the current atmosphere models are often not capable of fully explaining the spectra and luminosity of the sources. A particularly challenging component of the atmosphere models is the formation ... More

Fixed-parameter algorithms for minimum cost edge-connectivity augmentationApr 24 2013Aug 26 2013We consider connectivity-augmentation problems in a setting where each potential new edge has a nonnegative cost associated with it, and the task is to achieve a certain connectivity target with at most p new edges of minimum total cost. The main result ... More

Constraint satisfaction parameterized by solution sizeJun 21 2012Jan 18 2014In the constraint satisfaction problem (CSP) corresponding to a constraint language (i.e., a set of relations) $\Gamma$, the goal is to find an assignment of values to variables so that a given set of constraints specified by relations from $\Gamma$ is ... More

The method of double chains for largest families with excluded subposetsApr 24 2012For a given finite poset $P$, $La(n,P)$ denotes the largest size of a family $\mathcal{F}$ of subsets of $[n]$ not containing $P$ as a weak subposet. We exactly determine $La(n,P)$ for infinitely many $P$ posets. These posets are built from seven base ... More

Infinite combinatorics plain and simpleMay 17 2017Feb 05 2018We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly ... More

Finding small separators in linear time via treewidth reductionOct 21 2011We present a method for reducing the treewidth of a graph while preserving all of its minimal $s-t$ separators up to a certain fixed size $k$. This technique allows us to solve $s-t$ Cut and Multicut problems with various additional restrictions (e.g., ... More

Known Algorithms on Graphs of Bounded Treewidth are Probably OptimalJul 30 2010We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot ... More

Maps on positive definite matrices preserving Bregman and Jensen divergencesSep 08 2015In this paper we determine those bijective maps of the set of all positive definite $n\times n$ complex matrices which preserve a given Bregman divergence corresponding to a differentiable convex function that satisfies certain conditions. We cover the ... More

Near threshold laser-modified proton emission in nuclear photoeffectMar 06 2013Jun 25 2013The change of the probability of proton emission in nuclear photoeffect due to an intense coherent (laser) field is discussed near the threshold, where the hindering effect of the Coulomb field of the remainder nucleus is essential. The ratio of laser-assisted ... More

Properties of minimally $t$-tough graphsApr 10 2016A graph $G$ is minimally $t$-tough if the toughness of $G$ is $t$ and the deletion of any edge from $G$ decreases the toughness. Kriesell conjectured that for every minimally $1$-tough graph the minimum degree $\delta(G)=2$. We show that in every minimally ... More

Decomposing random graphs into few cycles and edgesApr 12 2014Nov 26 2014Over 50 years ago, Erd\H{o}s and Gallai conjectured that the edges of every graph on $n$ vertices can be decomposed into $O(n)$ cycles and edges. Among other results, Conlon, Fox and Sudakov recently proved that this holds for the random graph $G(n,p)$ ... More

Fixed-parameter Approximability of Boolean MinCSPsJan 19 2016The minimum unsatisfiability version of a constraint satisfaction problem asks for an assignment where the number of unsatisfied constraints is minimum possible, or equivalently, asks for a minimum-size set of constraints whose deletion makes the instance ... More

Rooted grid minorsJul 30 2013Intuitively, a tangle of large order in a graph is a highly-connected part of the graph, and it is known that if a graph has a tangle of large order then it has a large grid minor. Here we show that for any k, if G has a tangle of large order and Z is ... More

Treewidth reduction for constrained separation and bipartization problemsFeb 22 2009Feb 03 2010We present a method for reducing the treewidth of a graph while preserving all the minimal $s-t$ separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained separation and bipartization problems. ... More

$\mathcal{O}(k)$-robust spanners in one dimensionMar 23 2018A geometric $t$-spanner on a set of points in Euclidean space is a graph containing for every pair of points a path of length at most $t$ times the Euclidean distance between the points. Informally, a spanner is $\mathcal{O}(k)$-robust if deleting $k$ ... More

Squares and their centersAug 05 2014Aug 24 2014We study the relationship between the sizes of two sets $B, S\subset\mathbb{R}^2$ when $B$ contains either the whole boundary, or the four vertices, of a square with axes-parallel sides and center in every point of $S$, where size refers to one of cardinality, ... More

Union-intersecting set systemsMar 01 2014Three intersection theorems are proved. First, we determine the size of the largest set system, where the system of the pairwise unions is l-intersecting. Then we investigate set systems where the union of any s sets intersect the union of any t sets. ... More

Disorder is good for you: The influence of local disorder on strain localization and ductility of strain softening materialsApr 06 2016We formulate a generic concept model for the deformation of a locally disordered, macroscopically homogeneous material which undergoes irreversible strain softening during plastic deformation. We investigate the influence of the degree of microstructural ... More

Trustworthy Refactoring via Decomposition and Schemes: A Complex Case StudyAug 24 2017Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true confidence in ... More

Simulation of Pair Production in Extreme Strong EM FieldsMay 05 2012In this article we review a theoretical framework for pair production from strong external electromagnetic fields. We propose a numerical method to solve the resulting equations of motion and present results for both cases of spatially homogeneous and ... More

An improvement of the general bound on the largest family of subsets avoiding a subposetAug 25 2014Mar 16 2016Let $La(n,P)$ be the maximum size of a family of subsets of $[n]= \{1,2, ..., n \}$ not containing $P$ as a (weak) subposet, and let $h(P)$ be the length of a longest chain in $P$. The best known upper bound for $La(n,P)$ in terms of $|P|$ and $h(P)$ ... More

A measurement based software quality frameworkAug 14 2014Aug 17 2014In this report we propose a solution to problem of the dependency on the experience of the software project quality assurance personnel by providing a transparent, objective and measurement based quality framework. The framework helps the quality assurance ... More

Fixed-Parameter Tractability of Directed Multiway Cut Parameterized by the Size of the CutsetOct 03 2011Apr 25 2013Given a directed graph $G$, a set of $k$ terminals and an integer $p$, the \textsc{Directed Vertex Multiway Cut} problem asks if there is a set $S$ of at most $p$ (nonterminal) vertices whose removal disconnects each terminal from all other terminals. ... More

Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded TreewidthNov 26 2009We give the first polynomial-time approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, we show how to build a Steiner forest spanner for such graphs. The crux of ... More