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

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. © 2014 Wiley Periodicals, Inc. NETWORKS, 2014 Vol. 65(4), 353–366 2015