Approximating maximum edge coloring in multigraphs

Abstract

We study the complexity of the following problem that we call Max edge t-coloring: given a multigraph G and a parameter t, color as many edges as possible using t colors, such that no two adjacent edges are colored with the same color. (Equivalently, find the largest edge induced subgraph of G that has chromatic index at most t). We show that for every fixed t ≥ 2 there is some ε > 0 such that it is NP-hard to approximate Max edge t-coloring within a ratio better than 1−ε. We design approximation algorithms for the problem with constant factor approximation ratios. An interesting feature of our algorithms is that they allow us to estimate the value of the optimum solution up to a multiplicative factor that tends to 1 as t grows. Our study was motivated by call admittance issues in satellite based telecommunication networks.