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

Hao Huang; Benny Sudakov

doi:10.1007/s00493-012-2746-4

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

Hao Huang, Benny Sudakov

Research output: Contribution to journal › Article › peer-review

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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 language	English (US)
Pages (from-to)	205-219
Number of pages	15
Journal	Combinatorica
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s00493-012-2746-4
State	Published - Mar 2012
Externally published	Yes

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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author = "Hao Huang and Benny Sudakov",

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

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