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Beyond Submodular MaximizationApr 19 2019While there are well-developed tools for maximizing a submodular function subject to a matroid constraint, there is much less work on the corresponding supermodular maximization problems. We develop new techniques for attacking these problems inspired ... More

New results on pseudosquare avoidanceApr 19 2019We start by considering binary words containing the minimum possible numbers of squares and antisquares (where an antisquare is a word of the form $x \overline{x}$), and we completely classify which possibilities can occur. We consider avoiding $x p(x)$, ... More

Generalized threshold arrangementsApr 18 2019An arrangement of hyperplanes is a finite collection of hyperplanes in a real Euclidean space. To such a collection one associates the characteristic polynomial that encodes the combinatorics of intersections of the hyperplanes. Finding the characteristic ... More

Advancing Through TerrainsApr 18 2019We study terrain visibility graphs, a well-known graph class closely related to polygon visibility graphs in computational geometry, for which a precise graph-theoretical characterization is still unknown. Over the last decade, terrain visibility graphs ... More

Sesqui-Pushout Rewriting: Concurrency, Associativity and Rule Algebra FrameworkApr 17 2019Sesqui-pushout (SqPO) rewriting provides a variant of transformations of graph-like and other types of structures that fit into the framework of adhesive categories where deletion in unknown context may be implemented. We provide the first account of ... More

Circularly squarefree words and unbordered conjugates: a new approachApr 17 2019Using a new approach based on automatic sequences, logic, and a decision procedure, we reprove some old theorems about circularly squarefree words and unbordered conjugates in a new and simpler way. Furthermore, we prove three new results about unbordered ... More

The intersection of two vertex coloring problemsApr 17 2019A hole is an induced cycle with at least four vertices. A hole is even if its number of vertices is even. Given a set L of graphs, a graph G is L-free if G does not contain any graph in L as an induced subgraph. Currently, the following two problems are ... More

Inversion formula with hypergeometric polynomials and its application to an integral equationApr 16 2019For any complex parameters $x$ and $\nu$, we provide a new class of linear inversion formulas $T = A(x,\nu) \cdot S \Leftrightarrow S = B(x,\nu) \cdot T$ between sequences $S = (S_n)_{n \in \mathbb{N}^*}$ and $T = (T_n)_{n \in \mathbb{N}^*}$, where the ... More

On the Chromatic Polynomial and Counting DP-ColoringsApr 16 2019The chromatic polynomial of a graph $G$, denoted $P(G,m)$, is equal to the number of proper $m$-colorings of $G$. The list color function of graph $G$, denoted $P_{\ell}(G,m)$, is a list analogue of the chromatic polynomial that has been studied since ... More

Finding minimum locating arrays using a CSP solverApr 16 2019Combinatorial interaction testing is an efficient software testing strategy. If all interactions among test parameters or factors needed to be covered, the size of a required test suite would be prohibitively large. In contrast, this strategy only requires ... More

Efficiently Exploring Ordering Problems through Conflict-directed SearchApr 15 2019In planning and scheduling, solving problems with both state and temporal constraints is hard since these constraints may be highly coupled. Judicious orderings of events enable solvers to efficiently make decisions over sequences of actions to satisfy ... More

Combinatorial Conversion and Moment Bisimulation for Stochastic Rewriting SystemsApr 15 2019We develop a novel method to analyze the dynamics of stochastic rewriting systems evolving over finitary adhesive, extensive categories. Our formalism is based on the so-called rule algebra framework and exhibits an intimate relationship between the combinatorics ... More

A Linear Upper Bound on the Weisfeiler-Leman Dimension of Graphs of Bounded GenusApr 15 2019The Weisfeiler-Leman (WL) dimension of a graph is a measure for the inherent descriptive complexity of the graph. While originally derived from a combinatorial graph isomorphism test called the Weisfeiler-Leman algorithm, the WL dimension can also be ... More

The Bang Calculus and the Two Girard's TranslationsApr 15 2019We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call-by-name and call-by-value lambda-calculi to ... More

Linear algorithms on Steiner domination of treesApr 14 2019A set of vertices $W$ in a connected graph $G$ is called a Steiner dominating set if $W$ is both Steiner and dominating set. The Steiner domination number $\gamma_{st}(G)$ is the minimum cardinality of a Steiner dominating set of $G$. A linear algorithm ... More

Minimal Separators in GraphsApr 13 2019The Known Menger's theorem states that in a finite graph, the size of a minimum separator set of any pair of vertices is equal to the maximum number of disjoint paths that can be found between these two vertices. In this paper, we study the minimal separators ... More

Dominator Chromatic Numbers of Orientations of TreesApr 12 2019In this paper we prove that the dominator chromatic number of every oriented tree is invariant under reversal of orientation. In addition to this marquee result, we also prove the exact dominator chromatic number for arborescences and anti-arborescences ... More

The Perfect Matching Reconfiguration ProblemApr 12 2019We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of length four. ... More

Management of mobile resources in Physical Internet logistic modelsApr 12 2019This paper deals with the concept of a 'Physical Internet', the idea of building large logistics systems like the very successful Digital Internet network. The idea is to handle mobile resources, such as containers, just like Internet data packets. Thus, ... More

All quasitrivial n-ary semigroups are reducible to semigroupsApr 11 2019We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary semigroups. We also ... More

On the Displacement of Eigenvalues when Removing a Twin VertexApr 11 2019Twin vertices of a graph have the same common neighbours. If they are adjacent, then they are called duplicates and contribute the eigenvalue zero to the adjacency matrix. Otherwise they are termed co-duplicates, when they contribute $-1$ as an eigenvalue ... More

Prolific CompositionsApr 11 2019Under what circumstances might every extension of a combinatorial structure contain more copies of another one than the original did? This property, which we call prolificity, holds universally in some cases (e.g., finite linear orders) and only trivially ... More

Uniquely-Wilf classesApr 11 2019Two permutations in a class are Wilf-equivalent if, for every size, $n$, the number of permutations in the class of size $n$ containing each of them is the same. Those infinite classes that have only one equivalence class in each size for this relation ... More

Planar graphs have bounded nonrepetitive chromatic numberApr 10 2019A colouring of a graph is "nonrepetitive" if for every path of even order, the sequence of colours on the first half of the path is different from the sequence of colours on the second half. We show that planar graphs have nonrepetitive colourings with ... More

Cache-Aided Interference Management with Subexponential SubpacketizationApr 10 2019Consider an interference channel consisting of $K_T$ transmitters and $K_R$ receivers with AWGN noise and complex channel gains, and with $N$ files in the system. The one-shot $\mathsf{DoF}$ for this channel is the maximum number of receivers which can ... More

Planar Graphs have Bounded Queue-NumberApr 09 2019We show that planar graphs have bounded queue-number, thus proving a conjecture of Heath, Leighton and Rosenberg from 1992. The key to the proof is a new structural tool called layered $H$-partitions, and the result that every planar graph has such a ... More

On popularity-based random matching marketsApr 08 2019Stable matching in a community consisting of N men and N women is a classical combinatorial problem that has been the subject of intense theoretical and empirical study since its introduction in 1962 in a seminal paper by Gale and Shapley [GS62]. In this ... More

Linear-Time and Efficient Distributed Algorithms for List Coloring Graphs on SurfacesApr 07 2019In 1994, Thomassen proved that every planar graph is 5-list-colorable. In 1995, Thomassen proved that every planar graph of girth at least five is 3-list-colorable. His proofs naturally lead to quadratic-time algorithms to find such colorings. Here, we ... More

A characterization of maximal 2-dimensional subgraphs of transitive graphsApr 07 2019A transitive graph is 2-dimensional if it can be represented as the intersection of two linear orders. Such representations make answering of reachability queries trivial, and allow many problems that are NP-hard on arbitrary graphs to be solved in polynomial ... More

Semidefinite Programming in Timetabling and Mutual-Exclusion SchedulingApr 06 2019In scheduling and timetabling applications, the mutual-exclusion constraint stipulates that certain pairs of tasks that cannot be executed at the same time. This corresponds to the vertex colouring problem in graph theory, for which there are well-known ... More

$X$-Ramanujan GraphsApr 06 2019Apr 10 2019Let $X$ be an infinite graph of bounded degree; e.g., the Cayley graph of a free product of finite groups. If $G$ is a finite graph covered by $X$, it is said to be $X$-Ramanujan if its second-largest eigenvalue $\lambda_2(G)$ is at most the spectral ... More

Parameter estimation for integer-valued Gibbs distributionsApr 05 2019We consider the family of \emph{Gibbs distributions}, which are probability distributions over a discrete space $\Omega$ given by $\mu^\Omega_\beta(x)=\frac{e^{\beta H(x)}}{Z(\beta)}$. Here $H:\Omega\rightarrow \{0,1,\ldots,n\}$ is a fixed function (called ... More

Unavoidable minors for graphs with large $\ell_p$-dimensionApr 05 2019A metric graph is a pair $(G,d)$, where $G$ is a graph and $d:E(G) \to\mathbb{R}_{\geq0}$ is a distance function. Let $p \in [1,\infty]$ be fixed. An isometric embedding of the metric graph $(G,d)$ in $\ell_p^k = (\mathbb{R}^k, d_p)$ is a map $\phi : ... More

Reducing Topological Minor Containment to the Unique Linkage TheoremApr 05 2019In the Topological Minor Containment problem (TMC) problem two undirected graphs, $G$ and $H$ are given and the objective is to check whether $G$ contains $H$ as a topological minor. Grohe, Kawarabayashi, Marx, and Wollan~[STOC 2011] resolved the parameterized ... More

Normal $5$-edge-colorings of a family of Loupekhine snarksApr 04 2019In a proper edge-coloring of a cubic graph an edge $uv$ is called poor or rich, if the set of colors of the edges incident to $u$ and $v$ contains exactly three or five colors, respectively. An edge-coloring of a graph is normal, if any edge of the graph ... More

The Hamiltonicity, Hamiltonian Connectivity, and Longest (s, t)-path of L-shaped Supergrid GraphsApr 04 2019Supergrid graphs contain grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for general supergrid graphs were known to be NP-complete. A graph is called Hamiltonian if it contains a Hamiltonian cycle, and ... More

Boolean analysis of lateral inhibitionApr 04 2019We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in surrounding cells. ... More

An Integer Linear Programming Formulation for the Convex Dominating Set ProblemsApr 04 2019Due to their importance in practice, dominating set problems in graphs have been greatly studied in past and different formulations of these problems are presented in literature. This paper's focus is on two problems: weakly convex dominating set problem ... More

An Improved Upper Bound for the Ring Loading ProblemApr 03 2019The Ring Loading Problem emerged in the 1990s to model an important special case of telecommunication networks (SONET rings) which gained attention from practitioners and theorists alike. Given an undirected cycle on $n$ nodes together with non-negative ... More

The Satisfiability Threshold for Non-Uniform Random 2-SATApr 03 2019Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential Time Hypothesis. ... More

A spatial small-world graph arising from activity-based reinforcementApr 03 2019In the classical preferential attachment model, links form instantly to newly arriving nodes and do not change over time. We propose a hierarchical random graph model in a spatial setting, where such a time-variability arises from an activity-based reinforcement ... More

Combinatorial inequalitiesApr 02 2019This is an expanded version of the Notices of the AMS column with the same title. The text is unchanged, but we added acknowledgements and a large number of endnotes which provide the context and the references.

Towards a practical $k$-dimensional Weisfeiler-Leman algorithmApr 02 2019The $k$-dimensional Weisfeiler-Leman algorithm is a well-known heuristic for the graph isomorphism problem. Moreover, it recently emerged as a powerful tool for supervised graph classification. The algorithm iteratively partitions the set of $k$-tuples, ... More

An Algorithmic Theory of Integer ProgrammingApr 02 2019We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We show that integer ... More

On transitive uniform partitions of F^n into binary Hamming codesApr 02 2019We investigate transitive uniform partitions of the vector space $F^n$ of dimension $n$ over the Galois field $GF(2)$ into cosets of Hamming codes. A partition $P^n= \{H_0,H_1+e_1,\ldots,H_n+e_n\}$ of $F^n$ into cosets of Hamming codes $H_0,H_1,\ldots,H_n$ ... More

Decidability and Periodicity of Low Complexity TilingsApr 02 2019We investigate the tiling problem, also known as the domino problem, that asks whether the two-dimensional grid Z^2 can be colored in a way that avoids a given finite collection of forbidden local patterns. The problem is well-known to be undecidable ... More

Simplified inpproximability of hypergraph coloring via t-agreeing familiesApr 02 2019We reprove the results on the hardness of approximating hypergraph coloring using a different technique based on bounds on the size of extremal $t$-agreeing families of $[q]^n$. Specifically, using theorems of Frankl-Tokushige [FT99], Ahlswede-Khachatrian ... More

Approximation algorithms and an integer program for multi-level graph spannersApr 01 2019Given a weighted graph $G(V,E)$ and $t \ge 1$, a subgraph $H$ is a \emph{$t$--spanner} of $G$ if the lengths of shortest paths in $G$ are preserved in $H$ up to a multiplicative factor of $t$. The \emph{subsetwise spanner} problem aims to preserve distances ... More

Random walks and forbidden minors II: A $\text{poly}(d\varepsilon^{-1})$-query tester for minor-closed properties of bounded-degree graphsApr 01 2019Let $G$ be a graph with $n$ vertices and maximum degree $d$. Fix some minor-closed property $\mathcal{P}$ (such as planarity). We say that $G$ is $\varepsilon$-far from $\mathcal{P}$ if one has to remove $\varepsilon dn$ edges to make it have $\mathcal{P}$. ... More

Complexity and Algorithms for Semipaired Domination in GraphsApr 01 2019For a graph $G=(V,E)$ with no isolated vertices, a set $D\subseteq V$ is called a semipaired dominating set of G if $(i)$ $D$ is a dominating set of $G$, and $(ii)$ $D$ can be partitioned into two element subsets such that the vertices in each two element ... More

Some variations on Lyndon wordsApr 01 2019In this paper we compare two finite words $u$ and $v$ by the lexicographical order of the infinite words $u^\omega$ and $v^\omega$. Informally, we say that we compare $u$ and $v$ by the infinite order. We show several properties of Lyndon words expressed ... More

A More General Theory of Static Approximations for Conjunctive QueriesApr 01 2019Conjunctive query (CQ) evaluation is NP-complete, but becomes tractable for fragments of bounded hypertreewidth. Approximating a hard CQ by a query from such a fragment can thus allow for an efficient approximate evaluation. While underapproximations ... More

Boundedness of Conjunctive Regular Path QueriesApr 01 2019We study the boundedness problem for unions of conjunctive regular path queries with inverses (UC2RPQs). This is the problem of, given a UC2RPQ, checking whether it is equivalent to a union of conjunctive queries (UCQ). We show the problem to be ExpSpace-complete, ... More

Pebble Exchange Group of GraphsMar 31 2019A graph puzzle ${\rm Puz}(G)$ of a graph $G$ is defined as follows. A configuration of ${\rm Puz}(G)$ is a bijection from the set of vertices of a board graph $G$ to the set of vertices of a pebble graph $G$. A move of pebbles is defined as exchanging ... More

On the longest common subsequence of Thue-Morse wordsMar 30 2019The length $a(n)$ of the longest common subsequence of the $n$'th Thue-Morse word and its bitwise complement is studied. An open problem suggested by Jean Berstel in 2006 is to find a formula for $a(n)$. In this paper we prove new lower bounds on $a(n)$ ... More

Sparse graphs are near-bipartiteMar 29 2019A multigraph $G$ is near-bipartite if $V(G)$ can be partitioned as $I,F$ such that $I$ is an independent set and $F$ induces a forest. We prove that a multigraph $G$ is near-bipartite when $3|W|-2|E(G[W])|\ge -1$ for every $W\subseteq V(G)$, and $G$ contains ... More

Color Refinement, Homomorphisms, and HypergraphsMar 29 2019Recent results show that the structural similarity of graphs can be characterized by counting homomorphisms to them: the Tree Theorem states that the well-known color-refinement algorithm does not distinguish two graphs G and H if and only if, for every ... More

Nonlinear fourth order Taylor expansion of lattice Boltzmann schemesMar 29 2019We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms of a single infinitesimal numerical variable. The result is a system of partial differential equations for the conserved moments of the lattice Boltzmann scheme. ... More

Fractional matchings and component-factors of (edge-chromatic critical) graphsMar 29 2019The paper studies component-factors of graphs which can be characterized in terms of their fractional matching number. These results are used to prove that every edge-chromatic critical graph has a $[1,2]$-factor. Furthermore, fractional matchings of ... More

Arc-disjoint Strong Spanning Subdigraphs of Semicomplete CompositionsMar 28 2019A strong arc decomposition of a digraph $D=(V,A)$ is a decomposition of its arc set $A$ into two disjoint subsets $A_1$ and $A_2$ such that both of the spanning subdigraphs $D_1=(V,A_1)$ and $D_2=(V,A_2)$ are strong. Let $T$ be a digraph with $t$ vertices ... More

Sparse Reconstruction from Hadamard Matrices: A Lower BoundMar 28 2019We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. We show that for a $N \times N$ Hadamard matrix, one cannot recover ... More

An Improved Lower Bound for Sparse Reconstruction from Subsampled Hadamard MatricesMar 28 2019Apr 05 2019We give a short argument that yields a new lower bound on the number of subsampled rows from a bounded, orthonormal matrix necessary to form a matrix with the restricted isometry property. We show that a matrix formed by uniformly subsampling rows of ... More

Finding a planted clique by adaptive probingMar 28 2019We consider a variant of the planted clique problem where we are allowed unbounded computational time but can only investigate a small part of the graph by adaptive edge queries. We determine (up to logarithmic factors) the number of queries necessary ... More

Inconsistency indices for incomplete pairwise comparisons matricesMar 28 2019Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for determining the ... More

The minimum value of the Colless indexMar 27 2019The Colless index is one of the oldest and most widely used balance indices for rooted bifurcating trees. Despite its popularity, its minimum value on the space $\mathcal{T}_n$ of rooted bifurcating trees with $n$ leaves is only known when $n$ is a power ... More

The minimum value of the Colless indexMar 27 2019Apr 08 2019The Colless index is one of the oldest and most widely used balance indices for rooted bifurcating trees. Despite its popularity, its minimum value on the space $\mathcal{T}_n$ of rooted bifurcating trees with $n$ leaves is only known when $n$ is a power ... More

Cop number of $2K_2$-free graphsMar 27 2019We prove that the cop number of a $2K_2$-free graph is at most $2$ if it has diameter $3$ or does not have an induced cycle of length $k$, where $k \ \in \{3,4,5\}$. We conjecture that the cop number of every $2K_2$-free graph is at most $2$.

Convexly independent subsets of Minkowski sums of convex polygonsMar 27 2019We show that there exist convex $n$-gons $P$ and $Q$ such that the largest convex polygon in the Minkowski sum $P+Q$ has size $\Theta(n\log n)$. This matches an upper bound of Tiwary.

Scheduling Algorithms for 5G Networks with Mid-haul Capacity ConstraintsMar 27 2019We consider a virtualized RAN architecture for 5G networks where the Remote Units are connected to a central unit via a mid-haul. To support high data rates, the midhaul is realized with a Passive Optical Network (PON). In this architecture, the data ... More

On graphs with no induced five-vertex path or paragliderMar 27 2019Given two graphs $H_1$ and $H_2$, a graph is $(H_1,\,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ or $H_2$. For a positive integer $t$, $P_t$ is the chordless path on $t$ vertices. A paraglider is the graph that consists of a chorless ... More

Enumeration of irreducible and extended irreducible Goppa codesMar 26 2019We obtain upper bounds on the number of irreducible and extended irreducible Goppa codes over $GF(p)$ of length $q$ and $q+1$, respectively defined by polynomials of degree $r$, where $q=p^t$ and $r\geq 3$ is a positive integer.

Simultaneous Approximation of Measurement Values and Derivative Data using Discrete Orthogonal PolynomialsMar 26 2019This paper presents a novel method for polynomial approximation (Hermite approximation) using the fusion of value and derivative information. Therefore, the least-squares error in both domains is simultaneously minimized. A covariance weighting is used ... More

A linear bound on the k-rendezvous time for primitive sets of NZ matricesMar 25 2019A set of nonnegative matrices is called primitive if there exists a product of these matrices that is entrywise positive. Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest product of a ... More

A Reeb sphere theorem in graph theoryMar 25 2019We prove a Reeb sphere theorem for finite simple graphs. The result bridges two different definitions of spheres in graph theory. We also reformulate Morse conditions in terms of the center manifolds, the level surface graphs {f=f(x)} in the unit sphere ... More

An Exact No Free Lunch Theorem for Community DetectionMar 25 2019A precondition for a No Free Lunch theorem is evaluation with a loss function which does not assume a priori superiority of some outputs over others. A previous result for community detection by Peel et al. (2017) relies on a mismatch between the loss ... More

Cop throttling number: Bounds, values, and variantsMar 25 2019The cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and $capt_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the robber on $G$ over ... More

Density and Fractal Property of the Class of Oriented TreesMar 23 2019We show the density theorem for the class of finite oriented trees ordered by the homomorphism order. We also show that every interval of oriented trees, in addition to be dense, is in fact universal. We end by considering the fractal property in the ... More

Best-of-Three Voting on Dense GraphsMar 22 2019Given a graph $G$ of $n$ vertices, where each vertex is initially attached an opinion of either red or blue. We investigate a random process known as the Best-of-three voting. In this process, at each time step, every vertex chooses three neighbours at ... More

Permutation patterns in genome rearrangement problems: the reversal modelMar 20 2019In the context of the genome rearrangement problem, we analyze two well known models, namely the reversal and the prefix reversal models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$, we provide a ... More

Z_2-genus of graphs and minimum rank of partial symmetric matricesMar 20 2019The \emph{genus} $\mathrm{g}(G)$ of a graph $G$ is the minimum $g$ such that $G$ has an embedding on the orientable surface $M_g$ of genus $g$. A drawing of a graph on a surface is \emph{independently even} if every pair of nonadjacent edges in the drawing ... 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

Any Finite Distributive Lattice is Isomorphic to the Minimizer Set of an ${\rm M}^{\natural}$-Concave Set FunctionMar 20 2019Submodularity is an important concept in combinatorial optimization, and it is often regarded as a discrete analog of convexity. It is a fundamental fact that the set of minimizers of any submodular function forms a distributive lattice. Conversely, it ... More

Equitable partition of plane graphs with independent crossings into induced forestsMar 20 2019The cluster of a crossing in a graph drawing on the plane is the set of the four end-vertices of its two crossed edges. Two crossings are independent if their clusters do not intersect. In this paper, we prove that every plane graph with independent crossings ... More

A tighter bound on the number of relevant variables in a bounded degree Boolean functionMar 19 2019A classical theorem of Nisan and Szegedy says that a boolean function with degree $d$ as a real polynomial depends on at most $d2^{d-1}$ of its variables. In recent work by Chiarelli, Hatami and Saks, this upper bound was improved to $C \cdot 2^d$, where ... More

A tighter bound on the number of relevant variables in a bounded degree Boolean functionMar 19 2019Mar 21 2019A classical theorem of Nisan and Szegedy says that a boolean function with degree $d$ as a real polynomial depends on at most $d2^{d-1}$ of its variables. In recent work by Chiarelli, Hatami and Saks, this upper bound was improved to $C \cdot 2^d$, where ... More

Complexity of the dynamics of reaction systemsMar 19 2019Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena that complements ... More

Extending partial automorphisms of $n$-partite tournamentsMar 18 2019We prove that for every $n\geq 2$ the class of all finite $n$-partite tournaments (orientations of complete $n$-partite graphs) has the extension property for partial automorphisms, that is, for every finite $n$-partite tournament $G$ there is a finite ... More

Diversity in Combinatorial OptimizationMar 18 2019When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good solutions. ... More

The facets of the spanning trees polytopeMar 18 2019Let $G=(V, E)$ be an undirected graph. The spanning trees polytope $P(G)$ is the convex hull of the all spanning trees of $G$. In this paper, we describe all facets of $P(G)$ as a consequence of the facets of the bases polytope of a matroid.

A quantum cellular automaton for one-dimensional QEDMar 17 2019We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact gauge covariance ... More

On-Line Balancing of Random InputsMar 16 2019We consider an online vector balancing game where vectors $v_t$, chosen uniformly at random in $\{-1,+1\}^n$, arrive over time and a sign $x_t \in \{-1,+1\}$ must be picked immediately upon the arrival of $v_t$. The goal is to minimize the $L^\infty$ ... More

The mixing time of the swap (switch) Markov chains: a unified approachMar 15 2019Mar 19 2019Since 1997 a considerable effort has been spent to study the mixing time of \textbf{swap} (switch) Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained, ... More

The mixing time of the swap (switch) Markov chains: a unified approachMar 15 2019Since 1997 a considerable effort has been spent to study the mixing time of \textbf{swap} (switch) Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained, ... More

Proportionally dense subgraph of maximum size: complexity and approximationMar 15 2019Apr 10 2019We define a proportionally dense subgraph (PDS) as an induced subgraph of a graph with the property that each vertex in the PDS is adjacent to proportionally as many vertices in the subgraph as in the graph. We prove that the problem of finding a PDS ... More

On Cayley graphs of basic algebraic structuresMar 15 2019We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.

Limits of Sums for Binomial and Eulerian Numbers and their Associated DistributionsMar 15 2019We provide a unified, probabilistic approach using renewal theory to derive some novel limits of sums for the normalized binomial coefficients and for the normalized Eulerian numbers. We also investigate some corresponding results for their associated ... More

Profile Closeness in Complex NetworksMar 14 2019We introduce a new centrality measure, known as profile closeness, for complex networks. This network attribute originates from the graph-theoretic analysis of consensus problems. We also demonstrate its relevance in inferring the evolution of network ... More

An Exact Algorithm for Minimum Weight Vertex Cover Problem in Large GraphsMar 14 2019This paper proposes a novel branch-and-bound(BMWVC) algorithm to exactly solve the minimum weight vertex cover problem (MWVC) in large graphs. The original contribution is several new graph reduction rules, allowing to reduce a graph G and the time needed ... More

Highly irregular separated netsMar 14 2019In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study weaker notions of equivalence of separated nets and demonstrate that such ... More

A polynomial version of Cereceda's conjectureMar 13 2019Let $k$ and $d$ be such that $k \ge d+2$. Consider two $k$-colourings of a $d$-degenerate graph $G$. Can we transform one into the other by recolouring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that ... More