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 releva...

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Vydané v:Discrete mathematics and theoretical computer science Ročník 27:2; číslo Discrete Algorithms
Hlavní autori: Mömke, Tobias, Popa, Alexandru, Roshany-Tabrizi, Aida, Ruderer, Michael, Vincze, Roland
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Discrete Mathematics & Theoretical Computer Science 01.05.2025
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ISSN:1365-8050, 1365-8050
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Shrnutí: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 Comment: 24 pages, 6 figures, preliminary version published at WAOA 2023
ISSN:1365-8050
1365-8050
DOI:10.46298/dmtcs.13212