A counterexample to the Alon-Saks-Seymour conjecture and related problems

Details A counterexample to the Alon-Saks-Seymour conjecture and related problems A counterexample to the Alon-Saks-Seymour conjecture and related problems

2010-02-25

arxiv.org/abs/1002.4687v1

Mathematics

Combinatorics

Scientific paper

Consider a graph obtained by taking edge disjoint union of $k$ complete bipartite graphs. Alon, Saks and Seymour conjectured that such graph has chromatic number at most $k+1$. This well known conjecture remained open for almost twenty years. In this paper, we construct a counterexample to this conjecture and discuss several related problems in combinatorial geometry and communication complexity.

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