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arXiv · 1206.2384

Bounding the fractional chromatic number of $K_Δ$-free graphs

Katherine Edwards·Andrew D. King
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Abstract

King, Lu, and Peng recently proved that for $Δ\geq 4$, any $K_Δ$-free graph with maximum degree $Δ$ has fractional chromatic number at most $Δ-\tfrac{2}{67}$ unless it is isomorphic to $C_5\boxtimes K_2$ or $C_8^2$. Using a different approach we give improved bounds for $Δ\geq 6$ and pose several related conjectures. Our proof relies on a weighted local generalization of the fractional relaxation of Reed's $ω$, $Δ$, $χ$ conjecture.

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Katherine Edwards, Andrew D. King. 2013-03-30. Bounding the fractional chromatic number of $K_Δ$-free graphs. https://arxiv.org/abs/1206.2384

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