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The Fractional Chromatic Number of Zykov Products of Graphs

Abstract : Zykov designed one of the oldest known families of triangle-free graphs with arbitrarily high chromatic number. We determine the fractional chromatic number of the Zykov product of a family of graphs. As a corollary, we deduce that the fractional chromatic numbers of the Zykov graphs satisfy the same recurrence relation as those of the Mycielski graphs, that is a(n+1) = a(n) + 1/a(n). This solves a conjecture of Jacobs.
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Submitted on : Monday, January 24, 2011 - 2:25:46 PM
Last modification on : Tuesday, December 8, 2020 - 9:54:45 AM
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Pierre Charbit, Jean-Sébastien Sereni. The Fractional Chromatic Number of Zykov Products of Graphs. Applied Mathematics Letters, Elsevier, 2011, 24 (4), pp.432--437. ⟨10.1016/j.aml.2010.10.032⟩. ⟨hal-00558883⟩

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