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

Hao Huang, Benny Sudakov

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)205-219
Number of pages15
JournalCombinatorica
Volume32
Issue number2
DOIs
StatePublished - Mar 2012

Bibliographical note

Funding Information:
∗ Research supported in part by NSF CAREER award DMS-0812005 and by a USA-Israeli 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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