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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics