Improved edge-coloring with three colors

Authors:
Łukasz Kowalik
Affiliations:
Institute of Informatics, Warsaw University, Warsaw, Poland
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

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Abstract

We show an O(1.344n)=O(20.427 n) algorithm for edge-coloring an n-vertex graph using three colors. Our algorithm uses polynomial space. This improves over the previous, O(2n/2) algorithm of Beigel and Eppstein [1]. We extend 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.