The fractional chromatic number of Zykov products of graphs

Zykov designed one of the oldest known family 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 an+1 = an + 1 an . This solves a conjecture of Jacobs.

• Type: Journal
• Year: 2011
• Where: APPML
• Authors: Pierre Charbit, Jean-Sébastien Sereni
• Keywords: APPML 2011, Chromatic Numbers, Fractional Chromatic Numbers, Oldest Known Family, Software Engineering