New upper bounds on the chromatic number of a graph
Abstract
We outline some ongoing work related to a conjecture of Reed \cite{reed97} on $\omega$, $\Delta$, and $\chi$. We conjecture that the complement of a counterexample $G$ to Reed's conjecture has connectivity on the order of $\log(G)$. We prove that this holds for a family (parameterized by $\epsilon > 0$) of relaxed bounds; the $\epsilon = 0$ limit of which is Reed's upper bound.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606632
 Bibcode:
 2006math......6632R
 Keywords:

 Mathematics  Combinatorics;
 05C15;
 05C40;
 05C69