Approximating Maximum Edge 2-Coloring by Normalizing Graphs
<|reference_start|>Approximating Maximum Edge 2-Coloring by Normalizing Graphs: 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<|reference_end|>
@article{mömke2024approximating,
    title={Approximating Maximum Edge 2-Coloring by Normalizing Graphs},
    author={Tobias M"omke, Alexandru Popa, Aida Roshany-Tabrizi, Michael Ruderer,
  Roland Vincze},
    journal={arXiv preprint arXiv:2403.06691},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.06691},
    primaryClass={cs.DM cs.DS}
}