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Approximating the Maximum 3- and 4-Edge-Colorable Subgraph

(Extended Abstract)
  • Marcin Kamiński
  • Łukasz Kowalik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6139)

Abstract

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 K 4 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 K 3 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 K 5.

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.

Keywords

Approximation Algorithm Maximum Degree Approximation Ratio Simple Graph Colored Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marcin Kamiński
    • 1
  • Łukasz Kowalik
    • 2
  1. 1.Département d’InformatiqueUniversité Libre de Bruxelles 
  2. 2.Institute of InformaticsUniversity of Warsaw 

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