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Combinatorial Coloring of 3-Colorable Graphs

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2 Author(s)
Kawarabayashi, K. ; Nat. Inst. of Inf., Tokyo, Japan ; Thorup, M.

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(n4/11) colors. This is the first combinatorial improvement of Blum's Õ(n3/8) 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(n0.2072) colors by Chlamtac from FOCS'07. We now bring it down to Õ(n0. 2049) colors.

Published in:

Foundations of Computer Science (FOCS), 2012 IEEE 53rd Annual Symposium on

Date of Conference:

20-23 Oct. 2012

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