Kneser's Conjecture

A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up in the same class. Lovasz (1978) gave a proof based on graph theory. In particular, he showed that the Kneser graph, whose vertices represent the n-subsets, and where each edge connects two disjoint subsets, is not (k+1)-colorable. More precisely, his results says that the chromatic number is equal to k+2, and this...