, Volume 24, Issue 1, pp 163-170

A Combinatorial Proof of Kneser’s Conjecture*

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.

* Research supported by Charles University grants No. 158/99 and 159/99 and by ETH Zürich.