Related papers: On the Computational Complexity of the Bipartizing…
A matching cut of a graph is a partition of its vertex set in two such that no vertex has more than one neighbor across the cut. The Matching Cut problem asks if a graph has a matching cut. This problem, and its generalization d-cut, has…
List colouring is an NP-complete decision problem even if the total number of colours is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list colouring of permutation graphs with a bounded…
The Maximum Induced Matching problem asks to find the maximum $k$ such that, given a graph $G=(V,E)$, can we find a subset of vertices $S$ of size $k$ for which every vertices $v$ in the induced graph $G[S]$ has exactly degree $1$. In this…
A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a…
If $k\geq 0$, then a $k$-edge-coloring of a graph $G$ is an assignment of colors to edges of $G$ from the set of $k$ colors, so that adjacent edges receive different colors. A $k$-edge-colorable subgraph of $G$ is maximum if it is the…
In a bounded max-coloring of a vertex/edge weighted graph, each color class is of cardinality at most $b$ and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded max-vertex/edge-coloring problems ask for…
Given a graph $G$, two edges $e_{1},e_{2}\in E(G)$ are said to have a common edge $e$ if $e$ joins an endvertex of $e_{1}$ to an endvertex of $e_{2}$. A subset $B\subseteq E(G)$ is an edge open packing set in $G$ if no two edges of $B$ have…
A bipartite graph $G=(L,R;E)$ with at least one edge is said to be identifiable if for every vertex $v\in L$, the subgraph induced by its non-neighbors has a matching of cardinality $|L|-1$. An $\ell$-subgraph of $G$ is an induced subgraph…
We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that…
A class domination coloring (also called cd-Coloring or dominated coloring) of a graph is a proper coloring in which every color class is contained in the neighbourhood of some vertex. The minimum number of colors required for any…
In the Coloured Clustering problem, we wish to colour vertices of an edge coloured graph to produce as many stable edges as possible, i.e., edges with the same colour as their ends. In this paper, we reveal that the problem is in fact a…
In a graph $G$, let $\mu_G(xy)$ denote the number of edges between $x$ and $y$ in $G$. Let $\lambda K_{v,u}$ be the graph $(V\cup U,E)$ with $|V|=v$, $|U|=u$, and \[ \mu_G(xy)=\begin{cases} \lambda &\mbox{if $x\in U$ and $y\in V$ or if…
A \emph{co-bipartite chain} graph is a co-bipartite graph in which the neighborhoods of the vertices in each clique can be linearly ordered with respect to inclusion. It is known that the maximum cut problem (MaxCut) is NP-Hard in…
This paper explores the application of a new algebraic method of color exchanges to the edge coloring of simple graphs. Vizing's theorem states that the edge coloring of a simple graph $G$ requires either $\Delta$ or $\Delta+1$ colors,…
A b-coloring of the vertices of a graph is a proper coloring where each color class contains a vertex which is adjacent to at least one vertex in each other color class. The b-chromatic number of $G$ is the maximum integer $b(G)$ for which…
The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted…
A star edge coloring of a graph $G$ is a proper edge coloring with no 2-colored path or cycle of length four. The star edge coloring problem is to find an edge coloring of a given graph $G$ with minimum number $k$ of colors such that $G$…
The Exact Matching problem asks whether a bipartite graph with edges colored red and blue admits a perfect matching with exactly $t$ red edges. Introduced by Papadimitriou and Yannakakis in 1982, the problem has resisted deterministic…
A rainbow matching in an edge-colored graph is a matching whose edges have distinct colors. We address the complexity issue of the following problem, \mrbm: Given an edge-colored graph $G$, how large is the largest rainbow matching in $G$?…
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…