Alon-Saks-Seymour猜想的一个反例及相关问题
A counterexample to the Alon-Saks-Seymour conjecture and related problems
摘要：
考虑通过取$k$完全二部图的边不交并而得到的图。Alon，Saks和Seymour证明了这类图的色数至多为$k+1$ .这个著名的猜想仍然开放了近20年。本文构造了该猜想的一个反例，并讨论了组合几何和通信复杂性中的几个相关问题。
英文摘要：
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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