论文信息 - A Combinatorial Proof of Kneser's Conjecture

A Combinatorial Proof of Kneser's Conjecture

Kneser's conjecture, rst proved by Lovv asz in 1978, states that the graph with all k-element subsets of f1; 2; : : : ; ng 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.

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