Combinatorica

, Volume 24, Issue 1, pp 163–170

A Combinatorial Proof of Kneser’s Conjecture*

Original Paper

Kneser’s conjecture, first proved by Lovász in 1978, states that the graph with all k-element subsets of {1, 2, . . . , n} as vertices and with edges connecting disjoint sets has chromatic number n−2k+2. We derive this result from Tucker’s combinatorial lemma on labeling the vertices of special triangulations of the octahedral ball. By specializing a proof of Tucker’s lemma, we obtain self-contained purely combinatorial proof of Kneser’s conjecture.

Mathematics Subject Classification (2000):

05C15 05A05 55M35 

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Copyright information

© János Bolyai Mathematical Society 2004

Authors and Affiliations

  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic
  2. 2.Institut für InformatikETH ZentrumZürichSwitzerland

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