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Kneser's conjecture, chromatic number, and homotopy

https://doi.org/10.1016/0097-3165(78)90022-5Get rights and content
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Abstract

If the simplicial complex formed by the neighborhoods of points of a graph is (k − 2)-connected then the graph is not k-colorable. As a corollary Kneser's conjecture is proved, asserting that if all n-subsets of a (2n − k)-element set are divided into k + 1 classes, one of the classes contains two disjoint n-subsets.

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