Discrete Mathematics
Approximating Maximum Edge Coloring in Multigraphs
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
An asymptotic approximation scheme for multigraph edge coloring
ACM Transactions on Algorithms (TALG)
An improved approximation algorithm for maximum edge 2-coloring in simple graphs
Journal of Discrete Algorithms
Approximating maximum edge 2-coloring in simple graphs via local improvement
Theoretical Computer Science
Approximating the maximum 2- and 3-edge-colorable subgraph problems
Discrete Applied Mathematics
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We study large k-edge-colorable subgraphs of simple graphs and multigraphs. We show that: every simple subcubic graph G has a 3-edge-colorable subgraph (3-ECS) with at least $\frac{13}{15}|E(G)|$ edges, unless G is isomorphic to K4 with one edge subdivided, every subcubic multigraph G has a 3-ECS with at least $\frac{7}{9}|E(G)|$ edges, unless G is isomorphic to K3 with one edge doubled, every simple graph G of maximum degree 4 has a 4-ECS with at least $\frac{5}{6}|E(G)|$ edges, unless G is isomorphic to K5. We use these combinatorial results to design new approximation algorithms for the Maximum k-Edge-Colorable Subgraph problem. In particular, for k=3 we obtain a $\frac{13}{15}$-approximation for simple graphs and a $\frac{7}{9}$-approximation for multigraphs; and for k=4, we obtain a $\frac{9}{11}$-approximation. We achieve this by presenting a general framework of approximation algorithms that can be used for any value of k.