Mathematics Colloquia and Seminars

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Consider the problem of partitioning the $n$-element subsets of a $2n+k$-element set such that any two of the $n$-element subsets contained in the same partition class are pairwise intersecting. In 1955, Kneser showed that this can always be done with $k+2$ classes. He also conjectured that $k+2$ is the least possible number of classes in such a partition. This conjecture was open for several decades until Lovasz gave a proof using techniques in algebraic topology. I'll give a much simpler proof of this theorem due to Joshua Greene in 2002.