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2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2012)
New Brunswick, NJ, USA USA
Oct. 20, 2012 to Oct. 23, 2012
ISSN: 0272-5428
ISBN: 978-1-4673-4383-1
pp: 68-75
ABSTRACT
We consider the problem of coloring a 3-colorable graph in polynomial time using as few colors as possible. We present a combinatorial algorithm getting down to Õ(n^{4/11}) colors. This is the first combinatorial improvement of Blum's Õ(n^{3/8}) bound from FOCS'90. Like Blum's algorithm, our new algorithm composes nicely with recent semi-definite programming approaches. The current best bound is Õ(n^{0. 2072}) colors by Chlamtac from FOCS'07. We now bring it down to Õ(n^{0. 2049}) colors.
INDEX TERMS
Approximation Algorithms, Graph Coloring
CITATION
Ken-ichi Kawarabayashi, Mikkel Thorup, "Combinatorial Coloring of 3-Colorable Graphs", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 68-75, 2012, doi:10.1109/FOCS.2012.16
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