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The fractional chromatic number of Zykov products of graphs

✍ Scribed by Pierre Charbit; Jean Sébastien Sereni

Book ID
104001023
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
229 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

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 an . This solves a conjecture of Jacobs.

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