Approximating the maximum 2- and 3-edge-colorable subgraph problems

Authors:
Adrian Kosowski
Affiliations:
Department of Algorithms and System Modeling, Gdańsk University of Technology, Narutowicza 11/12, 80952 Gdańsk, Poland
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

For a fixed value of a parameter k=2, the Maximum k-Edge-Colorable Subgraph Problem consists in finding k edge-disjoint matchings in a simple graph, with the goal of maximising the total number of edges used. The problem is known to be APX-hard for all k, but there exist polynomial time approximation algorithms with approximation ratios tending to 1 as k tends to infinity. Herein we propose improved approximation algorithms for the cases of k=2 and k=3, having approximation ratios of 5/6 and 4/5, respectively.