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

Abstract

Consider a graph obtained by taking an edge disjoint union of k complete bipartite graphs. Alon, Saks, and Seymour conjectured that such graphs have 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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Correspondence to Hao Huang.

Additional information

Research supported in part by NSF CAREER award DMS-0812005 and by a USAIsraeli BSF grant. Research supported in part by NSF grant DMS-1101185, NSF CAREER award DMS-0812005, and by a USA-Israeli BSF grant.

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Huang, H., Sudakov, B. A counterexample to the Alon-Saks-Seymour conjecture and related problems. Combinatorica 32, 205–219 (2012). https://doi.org/10.1007/s00493-012-2746-4

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Mathematics Subject Classification (2000)

  • 05C15
  • 05C70
  • 68R05