Related papers: On the Minimum Chordal Completion Polytope
Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…
We prove that constant minimum degree already forces cycles with almost linearly many chords. Specifically, every graph $G$ with $\delta(G)\ge C$ contains a cycle of length $\ell\ge 4$ with $\Omega(\ell/\log^{C}\ell)$ chords for some…
We consider the following problem: for a given graph $G$ and two integers $k$ and $d$, can we apply a fixed graph operation at most $k$ times in order to reduce a given graph parameter $\pi$ by at least $d$? We show that this problem is…
In social networks the {\sc Strong Triadic Closure} is an assignment of the edges with strong or weak labels such that any two vertices that have a common neighbor with a strong edge are adjacent. The problem of maximizing the number of…
A graph operation that {\em contracts edges} is one of the fundamental operations in the theory of graph minors. Parameterized Complexity of editing to a family of graphs by contracting $k$ edges has recently gained substantial scientific…
In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a…
A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. In the manuscript "Coloring Meyniel graphs in linear time" we claimed that our algorithm MCColor produces an optimal coloring for every Meyniel…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
The Chordal Vertex Deletion (ChVD) problem asks to delete a minimum number of vertices from an input graph to obtain a chordal graph. In this paper we develop a polynomial kernel for ChVD under the parameterization by the solution size, as…
We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…
We initiate the study of computational complexity of graph coverings, aka locally bijective graph homomorphisms, for {\em graphs with semi-edges}. The notion of graph covering is a discretization of coverings between surfaces or topological…
A biclique in a graph $G$ is a complete bipartite subgraph (not necessarily induced), and the least positive integer $k$ for which the vertex set of $G$ can be partitioned into at most $k$ bicliques is the biclique vertex partition number…
Bipartite graphs are a fundamental concept in graph theory with diverse applications. A graph is bipartite iff it contains no odd cycles, a characteristic that has many implications in diverse fields ranging from matching problems to 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…
A cycle double cover (CDC) of an undirected graph is a collection of the graph's cycles such that every edge of the graph belongs to exactly two cycles. We describe a constructive method for generating all the cubic graphs that have a 6-CDC…
Containing many classic optimization problems, the family of vertex deletion problems has an important position in algorithm and complexity study. The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity.…
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…
A set of vertices in a graph is c-colorable if the subgraph induced by the set has a proper c-coloring. In this paper, we study the problem of finding a step-by-step transformation (reconfiguration) between two c-colorable sets in the same…
A labelled, undirected graph is a graph whose edges have assigned labels, from a specific set. Given a labelled, undirected graph, the well-known minimum labelling spanning tree problem is aimed at finding the spanning tree of the graph…
We consider incomplete pairwise comparison matrices and determine exactly when they have a consistent completion and, if not, when they have a nearly consistent completion. We use the maximum 3-cycle product as a measure of inconsistency…