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A combinatorial proof for the circular chromatic number of Kneser graphs

Author

Listed:
  • Daphne Der-Fen Liu

    (California State University, Los Angeles)

  • Xuding Zhu

    (Zhejiang Normal University)

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.

Suggested Citation

  • Daphne Der-Fen Liu & Xuding Zhu, 2016. "A combinatorial proof for the circular chromatic number of Kneser graphs," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 765-774, October.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:3:d:10.1007_s10878-015-9897-3
    DOI: 10.1007/s10878-015-9897-3
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    Cited by:

    1. C. M. H. de Figueiredo & C. S. R. Patrão & D. Sasaki & M. Valencia-Pabon, 2022. "On total and edge coloring some Kneser graphs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 119-135, August.

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