Approximating Maximum Edge 2-Coloring by Normalizing Graphs
Abstract
In a simple, undirected graph G, an edge 2-coloring is a coloring of the edges such that no vertex is incident to edges with more than 2 distinct colors. The problem maximum edge 2-coloring (ME2C) is to find an edge 2-coloring in a graph G with the goal to maximize the number of colors. For a relevant graph class, ME2C models anti-Ramsey numbers and it was considered in network applications. For the problem a 2-approximation algorithm is known, and if the input graph has a perfect matching, the same algorithm has been shown to have a performance guarantee of 5/3. It is known that ME2C is APX-hard and that it is UG-hard to obtain an approximation ratio better than 1.5. We show that if the input graph has a perfect matching, there is a polynomial time 1.625-approximation and if the graph is claw-free or if the maximum degree of the input graph is at most three (i.e., the graph is subcubic), there is a polynomial time 1.5-approximation algorithm for ME2C
Keywords
Cite
@article{arxiv.2403.06691,
title = {Approximating Maximum Edge 2-Coloring by Normalizing Graphs},
author = {Tobias Mömke and Alexandru Popa and Aida Roshany-Tabrizi and Michael Ruderer and Roland Vincze},
journal= {arXiv preprint arXiv:2403.06691},
year = {2025}
}
Comments
24 pages, 6 figures, preliminary version published at WAOA 2023