Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ $k\ge 5$. The list problem asks following more general question: given available colors each vertex in graph, does it admit proper coloring? We propose quantum based Grover search to quadratically speed up exhaustive search...

In this paper, we study the conflict-free coloring of graphs induced by neighborhoods. A coloring of a graph is conflict-free if every vertex has a uniquely colored vertex in its neighborhood. The conflict-free coloring problem is to color the vertices of a graph using the minimum number of colors such that the coloring is conflict-free. We consider both closed neighborhoods, where the neighbor...

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...

In this paper we propose a deterministic parallel graph coloring algorithm that enables Multi-Coloring in parallel for sparse undirected graphs by coarse-grained segmentation and auxiliary graph coloring. The proposed algorithm is implemented and tested on standard problem instances from engineering applications and benchmarked against various relevant deterministic graph coloring algorithms. Q...

Given an n-vertex graph G and two positive integers d, k ∈ N, the (d, kn)-differential coloring problem asks for a coloring of the vertices of G (if one exists) with distinct numbers from 1 to kn (treated as colors), such that the minimum difference between the two colors of any adjacent vertices is at least d. While it was known that the problem of determining whether a general graph is (2, n)...

Graph coloring problem (GCP) is one of the most studied combinatorial optimization problems. It is important in theory and practice. There have been many algorithms for graph coloring problem, including exact algorithms and (meta-)heuristic algorithms. In this paper, we attempt another meta-heuristic method⎯particle swarm optimization to graph coloring problem. Particle swarm optimization (PSO)...

Abs t r ac t . In an edge-coloring of a graph G = (V, E) each color appears around each vertex at most once. An f-coloring is a generalization of an edge-coloring in which each color appears around each vertex v at most f(v) times where f is a function assigning a natural number f(v) e N to each vertex v E V. In this paper we first give a simple reduction of the f-coloring problem to the ordina...