Related papers: On the Parameterized Complexity of the Maximum Edg…
The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…
In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper $r$-coloring $\varphi$ of a graph $G$. We investigate the problem of finding a proper $r$-coloring of $G$, which is "the…
This paper investigates an extremely classic NP-complete problem: How to determine if a graph G, where each vertex has a degree of at most 4, can be 3-colorable(The research in this paper focuses on graphs G that satisfy the condition where…
Given a graph $G$, a proper $k$-coloring of $G$ is a partition $c = (S_i)_{i\in [1,k]}$ of $V(G)$ into $k$ stable sets $S_1,\ldots, S_{k}$. Given a weight function $w: V(G) \to \mathbb{R}^+$, the weight of a color $S_i$ is defined as $w(i)…
Let $c, k$ be two positive integers and let $G=(V,E)$ be a graph. The $(c,k)$-Load Coloring Problem (denoted $(c,k)$-LCP) asks whether there is a $c$-coloring $\varphi: V \rightarrow [c]$ such that for every $i \in [c]$, there are at least…
The semistrong edge coloring, as a relaxation of the well-known strong edge coloring, can be used to model efficient communication scheduling in wireless networks. An edge coloring of a graph $G$ is called \emph{semistrong} if every color…
In this paper, we consider a weighted generalization of the chromatic number of a Binomial random graph~\(G.\) We equip each edge with a random weight and then colour the vertices in such a way that the absolute colour difference between…
We study the parameterized complexity of the $s$-Club Cluster Edge Deletion problem: Given a graph $G$ and two integers $s \ge 2$ and $k \ge 1$, is it possible to remove at most $k$ edges from $G$ such that each connected component of the…
The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being…
A graph on $n$ vertices is equitably $k$-colorable if it is $k$-colorable and every color is used either $\left\lfloor n/k \right\rfloor$ or $\left\lceil n/k \right\rceil$ times. Such a problem appears to be considerably harder than vertex…
In this paper, we initiate the study of the vertex coloring problem of a graph in the semi streaming model. In this model, the input graph is defined by a stream of edges, arriving in adversarial order and any algorithm must process the…
In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an undirected graph $G$, a positive integer…
The quest for colorful components (connected components where each color is associated with at most one vertex) inside a vertex-colored graph has been widely considered in the last ten years. Here we consider two variants, Minimum Colorful…
In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a…
In this paper we study the complexity of the following problems: Given a colored graph X=(V,E,c), compute a minimum cardinality set S of vertices such that no nontrivial automorphism of X fixes all vertices in S. A closely related problem…
Given a wireless network where some pairs of communication links interfere with each other, we study sufficient conditions for determining whether a given set of minimum bandwidth Quality of Service (QoS) requirements can be satisfied. We…
We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…
We study the parameterized complexity of interdiction problems in graphs. For an optimization problem on graphs, one can formulate an interdiction problem as a game consisting of two players, namely, an interdictor and an evader, who…
Given a straight-line drawing of a graph, a segment is a maximal set of edges that form a line segment. Given a planar graph $G$, the segment number of $G$ is the minimum number of segments that can be achieved by any planar straight-line…
In this paper, we study several coloring problems on graphs from the viewpoint of parameterized complexity. We show that Precoloring Extension is fixed-parameter tractable (FPT) parameterized by distance to clique and Equitable Coloring is…