In a previous work, we proposed a new integer programming formulation for the graph coloring problem which, to a certain extent, avoids symmetry. We studied the facet structure of the 0/1-polytope associated with it. Based on these theoretical results, we present now a Branch-and-Cut algorithm for the graph coloring problem. Our computational experiences compare favorably with the well-known ex...

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

Coloring of a graph is an assignment of colors either to the edges of the graph G, or to vertices, or to maps in such a way that adjacent edges/vertices/maps are colored differently. We consider the problem of coloring graphs by using webMathematica which is the new web-based technology. In this paper, we describe some web-based interactive examples on graph coloring with webMathematica.

Graph coloring is a fundamental graph problem that is widely applied in a variety of applications. The aim of graph coloring is to minimize the number of colors used to color the vertices in a graph such that no two incident vertices have the same color. Existing solutions for graph coloring mainly focus on computing a good coloring for a static graph. However, since many real-world graphs are ...

This paper is concerned with algorithms and complexity results for defective coloring, where a defective (k; d)-coloring is a k coloring of the vertices of a graph such that each vertex is adjacent to at most d-self-colored neighbors. First, (2; d) coloring is shown NP-complete for d 1, even for planar graphs, and (3; 1) coloring is also shown NP-complete for planar graphs (while there exists a...

We describe an approach to optimization based on a multiple-restart quasi-Hopfield network where the only problem-specific knowledge is embedded in the energy function that the algorithm tries to minimize. We apply this method to three different variants of the graph coloring problem: the minimum coloring problem, the spanning subgraph k-coloring problem, and the induced subgraph k-coloring pro...

Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology, and the framework through which it was studied, we introduce the colinear coloring on graphs. We provide an upper bound for the chromatic number χ(G), for any graph G, and show that G can be colinearly colored in polynomial time by proposing a simple algorithm. The c...

Abstract. We study the maximum differential graph coloring problem, in which the goal is to find a vertex labeling for a given undirected graph that maximizes the label difference along the edges. This problem has its origin in map coloring, where not all countries are necessarily contiguous. We define the differential chromatic number and establish the equivalence of the maximum differential c...

An equitable k-coloring of a graph is defined by a partition of its vertices into k disjoint stable subsets, such that the difference between the cardinalities of any two subsets is at most one. The equitable coloring problem consists of finding the minimum value of k such that a given graph can be equitably k-colored. We present two new integer programming formulations based on representatives...