, Volume 24, Issue 1, pp 163–170

A Combinatorial Proof of Kneser’s Conjecture*


    • Department of Applied MathematicsCharles University
    • Institut für InformatikETH Zentrum
Original Paper

DOI: 10.1007/s00493-004-0011-1

Cite this article as:
Matoušek, J. Combinatorica (2004) 24: 163. doi:10.1007/s00493-004-0011-1

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):


Copyright information

© János Bolyai Mathematical Society 2004