2012 IEEE 53rd 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

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2012.16

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

K. Kawarabayashi and M. Thorup, "Combinatorial Coloring of 3-Colorable Graphs,"

*2012 IEEE 53rd Annual Symposium on Foundations of Computer Science(FOCS)*, New Brunswick, NJ, USA USA, 2012, pp. 68-75.

doi:10.1109/FOCS.2012.16

CITATIONS