B. Reed

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20032012

most citedMinima in branching random walks

101 citations · 125 across the 7 of their papers we have counts for

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cs.DM2012

Claw-free graphs, skeletal graphs, and a stronger conjecture on $ω$ , $Δ$ , and $χ$

Andrew D. King, Bruce A. Reed

The second author's $ω$ , $Δ$ , $χ$ conjecture proposes that every graph satisties $χ \leq ⌈ \frac{1}{2} (Δ + 1 + ω)⌉$ . In this paper we prove that the conjecture holds for all cla…

cs.DM2012

A short proof that $χ$ can be bounded $ε$ away from $Δ + 1$ towards $ω$

Andrew D. King, Bruce A. Reed

In 1998 the second author proved that there is an $ε > 0$ such that every graph satisfies $χ \leq ⌈(1 - ε) (Δ + 1) + ε ω ⌉$ . The first author recently proved that any graph satisfyi…

cs.DM2011

Asymptotics of the chromatic number for quasi-line graphs

Andrew D. King, Bruce Reed

As proved by Kahn, the chromatic number and fractional chromatic number of a line graph agree asymptotically. That is, for any line graph $G$ we have $χ (G) \leq (1 + o (1)) χ_{f} (G)$ . We…

Claw-free graphs, skeletal graphs, and a stronger conjecture on ω, Δ, and χ

A short proof that χ can be bounded ε away from Δ+1 towards ω

Asymptotics of the chromatic number for quasi-line graphs

Claw-free graphs, skeletal graphs, and a stronger conjecture on $ω$ , $Δ$ , and $χ$

A short proof that $χ$ can be bounded $ε$ away from $Δ + 1$ towards $ω$