New upper bounds on the chromatic number of a graph

Details New upper bounds on the chromatic number of a graph New upper bounds on the chromatic number of a graph

2006-06-25

arxiv.org/abs/math/0606632v1

Mathematics

Combinatorics

Scientific paper

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.

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