Related papers: A color-avoiding approach to subgraph counting in …

Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…

A square coloring of a graph $G$ is a coloring of the square $G^2$ of $G$, that is, a coloring of the vertices of $G$ such that any two vertices that are at distance at most $2$ in $G$ receive different colors. We investigate the complexity…

An injective edge-coloring $c$ of a graph $G$ is an edge-coloring such that if $e_1$, $e_2$, and $e_3$ are three consecutive edges in $G$ (they are consecutive if they form a path or a cycle of length three), then $e_1$ and $e_3$ receive…

Call a simple graph $H$ of order $n$ well-separable, if by deleting a separator set of size $o(n)$ the leftover will have components of size at most $o(n)$. We prove, that bounded degree well-separable spanning subgraphs are easy to embed:…

We investigate the problem $\#\mathsf{IndSub}(\Phi)$ of counting all induced subgraphs of size $k$ in a graph $G$ that satisfy a given property $\Phi$. This continues the work of Jerrum and Meeks who proved the problem to be…

Given a graph $G$ and a nondecreasing sequence $S=(s_1,\ldots,s_k)$ of positive integers, the mapping $c:V(G)\longrightarrow \{1,\ldots,k\}$ is called an $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in…

Computing the smallest number $q$ such that the vertices of a given graph can be properly $q$-colored is one of the oldest and most fundamental problems in combinatorial optimization. The $q$-Coloring problem has been studied intensively…

The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subject to the constraint that no H subgraph is…

We study the computational complexity of the problem $\#\text{IndSub}(\Phi)$ of counting $k$-vertex induced subgraphs of a graph $G$ that satisfy a graph property $\Phi$. Our main result establishes an exhaustive and explicit classification…

The question to enumerate all inclusion-minimal connected dominating sets in a graph of order $n$ in time significantly less than $2^n$ is an open question that was asked in many places. We answer this question affirmatively, by providing…

Given a connected graph $G$ and its vertex $x$, let $U_x(G)$ denote the universal cover of $G$ obtained by unfolding $G$ into a tree starting from $x$. Let $T=T(n)$ be the minimum number such that, for graphs $G$ and $H$ with at most $n$…

A graph class is $\chi$-bounded if the only way to force large chromatic number in graphs from the class is by forming a large clique. In the 1970s, Erd\H{o}s conjectured that intersection graphs of straight-line segments in the plane are…

Dujmovi\'c et al (FOCS2019) recently proved that every planar graph $G$ is a subgraph of $H\boxtimes P$, where $\boxtimes$ denotes the strong graph product, $H$ is a graph of treewidth 8 and $P$ is a path. This result has found numerous…

For an undirected graph G, we consider the following problems: given a fixed graph H, can we partition the vertices of G into two non-empty sets A and B such that neither the induced graph G[A] nor G[B] contain H (i) as a subgraph? (ii) as…

Generalizing the notion of split graphs to uniform hypergraphs, we prove that the class of these hypergraphs can be characterized by a finite list of excluded induced subhypergraphs. We show that a characterization by generalized degree…

We study a random graph $G$ with given degree sequence $\boldsymbol{d}$, with the aim of characterising the degree sequence of the subgraph induced on a given set $S$ of vertices. For suitable $\boldsymbol{d}$ and $S$, we show that the…

We study graph classes modeled by families of non-crossing (NC) connected sets. Two classic graph classes in this context are disk graphs and proper interval graphs. We focus on the cases when the sets are paths and the host is a tree…

Hypergraphs offer flexible and robust data representations for many applications, but methods that work directly on hypergraphs are not readily available and tend to be prohibitively expensive. Much of the current analysis of hypergraphs…

The \textit{longest path transversal number} of a connected graph $G$, denoted by $lpt(G)$, is the minimum size of a set of vertices of $G$ that intersects all longest paths in $G$. We present constant upper bounds for the longest path…

Computing a dense subgraph is a fundamental problem in graph mining, with a diverse set of applications ranging from electronic commerce to community detection in social networks. In many of these applications, the underlying context is…