Fractional chromatic number, maximum degree and girth

Abstract : We prove new lower bounds on the independence ratio of graphs of maximum degree ∆ ∈ {3, 4, 5} and girth g ∈ {6,. .. , 12}, notably 1/3 when (∆,g)=(4, 10) et 2/7 when (∆,g)=(5, 8). We also demonstrate that every graph of girth at least 7 and maximum degree ∆ has fractional chromatic number at most min (2∆+2 k−3 +k)/k over k∈N. In particular, the fractional chromatic number of a graph of girth 7 and maximum degree ∆ is at most (2∆+9)/5 when ∆ ∈ [3, 8], at most (∆+7)/3 when ∆ ∈ [8, 20], at most (2∆+23)/7 when ∆ ∈ [20, 48], and at most ∆/4 + 5 when ∆ ∈ [48, 112].
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https://hal.archives-ouvertes.fr/hal-02096426
Contributor : Jean-Sébastien Sereni <>
Submitted on : Sunday, April 21, 2019 - 10:08:40 AM
Last modification on : Wednesday, April 24, 2019 - 1:39:10 AM

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  • HAL Id : hal-02096426, version 2

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François Pirot, Jean-Sébastien Sereni. Fractional chromatic number, maximum degree and girth. 2019. ⟨hal-02096426v2⟩

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