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An application of principal bundles to coloring of graphs and hypergraphs

Milgram, James R.Zvengrowski, Peter — 1994

Proceedings of the Winter School "Geometry and Physics"

An interesting connection between the chromatic number of a graph G and the connectivity of an associated simplicial complex N ( G ) , its “neighborhood complex”, was found by Lovász in 1978 (cf. [J. Comb. Theory, Ser. A 25, 319-324 (1978; Zbl 0418.05028)]). In 1986 a generalization to the chromatic number of a k -uniform hypergraph H , for k an odd prime, using an associated simplicial complex C ( H ) , was found ([, and , Trans. Am. Math. Soc. 298, 359-370 (1986; Zbl 0605.05033)], Prop. 2.1). It was already...

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