A combinatorial proof for the circular chromatic number of Kneser graphs

Daphne Der-Fen Liu () and Xuding Zhu ()
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Daphne Der-Fen Liu: California State University, Los Angeles
Xuding Zhu: Zhejiang Normal University

Journal of Combinatorial Optimization, 2016, vol. 32, issue 3, No 7, 765-774

Abstract: Abstract Chen (J Combin Theory A 118(3):1062–1071, 2011) confirmed the Johnson–Holroyd–Stahl conjecture that the circular chromatic number of a Kneser graph is equal to its chromatic number. A shorter proof of this result was given by Chang et al. (J Combin Theory A 120:159–163, 2013). Both proofs were based on Fan’s lemma (Ann Math 56:431–437, 1952) in algebraic topology. In this article we give a further simplified proof of this result. Moreover, by specializing a constructive proof of Fan’s lemma by Prescott and Su (J Combin Theory A 111:257–265, 2005), our proof is self-contained and combinatorial.

Keywords: Chromatic number; Circular chromatic number; Kneser graphs (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9897-3

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