The Fractional Chromatic Number of Zykov Products of Graphs

Pierre Charbit (1) , Jean-Sébastien Sereni (1, 2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 KAM - Department of Applied Mathematics (KAM)

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.

Mots clés: Fractional coloring; Zykov graphs; Triangle-free graphs

Domaines: Mathématique discrète [cs.DM]

Pierre Charbit, Jean-Sébastien Sereni. The Fractional Chromatic Number of Zykov Products of Graphs. Applied Mathematics Letters, 2011, 24 (4), pp.432--437. ⟨10.1016/j.aml.2010.10.032⟩. ⟨hal-00558883⟩