A branch‐and‐price algorithm for the (k,c)‐coloring problem

Abstract

In this article, we study the (k,c)-coloring problem, a generalization of the vertex coloring problem where we have to assign k colors to each vertex of an undirected graph, and two adjacent vertices can share at most c colors. We propose a new formulation for the (k,c)-coloring problem and develop a Branch-and-Price algorithm. We tested the algorithm on instances having from 20 to 80 vertices and different combinations for k and c, and compare it with a recent algorithm proposed in the literature. Computational results show that the overall approach is effective and has very good performance on instances where the previous algorithm fails.

Preface

“…Malaguti et al study a generalization of the vertex coloring problem where k colors need to be assigned to each vertex of an undirected graph, and two adjacent vertices can share at most c colors. The authors propose a new formulation for the problem, develop a branch‐and‐price algorithm, and analyze computational results.…”