Improved edge-coloring with three colors

Authors:
ukasz Kowalik
Affiliations:
Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland and Max-Planck-Institute für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We show an O(1.344^n)=O(2^0^.^4^2^7^n) algorithm for edge-coloring an n-vertex graph using three colors. Our algorithm uses polynomial space. This improves over the previous O(2^n^/^2) algorithm of Beigel and Eppstein [R. Beigel, D. Eppstein, 3-coloring in time O(1.3289n), J. Algorithms 54 (2) (2005) 168-204.]. We apply a very natural approach of generating inclusion-maximal matchings of the graph. The time complexity of our algorithm is estimated using the ''measure and conquer'' technique.