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One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…
The problem of graph Reachability is to decide whether there is a path from one vertex to another in a given graph. In this paper, we study the Reachability problem on three distinct graph families - intersection graphs of Jordan regions,…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
This paper investigates the computational complexity of deciding whether the vertices of a graph can be partitioned into a disjoint union of cliques and a triangle-free subgraph. This problem is known to be $\NP$-complete on arbitrary…
A straight-line drawing $\delta$ of a planar graph $G$ need not be plane, but can be made so by \emph{untangling} it, that is, by moving some of the vertices of $G$. Let shift$(G,\delta)$ denote the minimum number of vertices that need to…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture postulates that every graph of order at least 3 is reconstructible. We show that interval graphs…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
A $k$-coloring of a graph is an assignment of integers between $1$ and $k$ to vertices in the graph such that the endpoints of each edge receive different numbers. We study a local variation of the coloring problem, which imposes further…
Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the…
Given a property (graph class) $\Pi$, a graph $G$, and an integer $k$, the \emph{$\Pi$-completion} problem consists in deciding whether we can turn $G$ into a graph with the property $\Pi$ by adding at most $k$ edges to $G$. The…
Let $S=\{K_{1,3},K_3,P_4\}$ be the set of connected graphs of size 3. We study the problem of partitioning the edge set of a graph $G$ into graphs taken from any non-empty $S'\subseteq S$. The problem is known to be NP-complete for any…
Vertex deletion problems for graphs are studied intensely in classical and parameterized complexity theory. They ask whether we can delete at most k vertices from an input graph such that the resulting graph has a certain property.…
Partitioning a graph into blocks of "roughly equal" weight while cutting only few edges is a fundamental problem in computer science with a wide range of applications. In particular, the problem is a building block in applications that…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…
Flip graphs are a ubiquitous class of graphs, which encode relations induced on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance, are the graphs induced by quadrilateral flips in…
A vertex subset $I$ of a graph $G$ is called a $k$-path vertex cover if every path on $k$ vertices in $G$ contains at least one vertex from $I$. The \textsc{$k$-Path Vertex Cover Reconfiguration ($k$-PVCR)} problem asks if one can transform…
Let $G$ be a graph having a vertex $v$ such that $H = G - v$ is a trivially perfect graph. We give a polynomial-time algorithm for the problem of deciding whether it is possible to add at most $k$ edges to $G$ to obtain a trivially perfect…
In this paper we deal with the Bin Packing Problem with Conflicts on interval graphs: given an interval graph, a nonnegative integer weight for each vertex, and a nonnegative integer B, find a partition of the vertex set of the graph into k…