Related papers: A Note on Graphs with 2 Bends
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
In this paper, we generalize the concept of complete coloring and achromatic number to 2-edge-colored graphs and signed graphs. We give some useful relationships between different possible definitions of such achromatic numbers and prove…
Given a set of objects $O$ in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit…
We show that P2T - the problem of deciding whether the edge set of a simple graph can be partitioned into two trees or not - is NP-complete.
The presented material is devoted to the equivalent conversion from the vertex graphs to the edge graphs. We suggest that the proved theorems solve the problem of the isomorphism of graphs, the problem of the graph's enumeration with the…
The 2-colorable perfect matching problem asks whether a graph can be colored with two colors so that each node has exactly one neighbor with the same color as itself. We prove that this problem is NP-complete, even when restricted to…
The class of 2-interval graphs has been introduced for modelling scheduling and allocation problems, and more recently for specific bioinformatic problems. Some of those applications imply restrictions on the 2-interval graphs, and justify…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
This note is on the structures of line graphs and 2-variegated graphs. We have given here solutions of some graph equations involving line graphs and 2-variegated graphs.
An EPG-representation of a graph $G$ is a collection of paths in a plane square grid, each corresponding to a single vertex of $G$, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In…
Two decision problems related to the computation of stopping sets in Tanner graphs are shown to be NP-complete. NP-hardness of the problem of computing the stopping distance of a Tanner graph follows as a consequence
In this paper, we generalize the notions of perfect matchings, perfect 2-matchings to perfect k-matchings and give a necessary and sufficient condition for existence of perfect k-matchings. For bipartite graphs, we show that this k-matching…
We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
In this paper, we consider the problem of a star coloring. In general case the problems in NP-complete. We establish the star chromatic number for splitting graph of complete and complete bipartite graphs, as well of paths and cycles. Our…
The \emph{thinness} of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Graphs with thinness at most two include, for example, bipartite convex graphs. Many…
Motivated by investigations of rainbow matchings in edge colored graphs, we introduce the notion of color-line graphs that generalizes the classical concept of line graphs in a natural way. Let $H$ be a (properly) edge-colored graph. The…
We investigate edge-intersection graphs of paths in the plane grid, regarding a parameter called the bend-number. I.e., every vertex is represented by a grid path and two vertices are adjacent if and only if the two grid paths share at…
A complete graph is the graph in which every two vertices are adjacent. For a graph $G=(V,E)$, the complete width of $G$ is the minimum $k$ such that there exist $k$ independent sets $\mathtt{N}_i\subseteq V$, $1\le i\le k$, such that the…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…