On a theorem of Lovász on covers in r-partite hypergraphs

Ron Aharoni*, Ron Holzman, Michael Krivelevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A theorem of Lovász asserts that τ(H)/τ* (H)≤r/2 for every r-partite hypergraph H (where τ and τ* denote the covering number and fractional covering number respectively). Here it is shown that the same upper bound is valid for a more general class of hypergraphs: those which admit a partition (V1,...,Vk) of the vertex set and a partition p1 +...+ pk of r such that |e∩Vi|≤pi≤r/2 for every edge e and every 1≤i≤k. Moreover, strict inequality holds when r>2, and in this form the bound is tight. The investigation of the ratio τ/τ* is extended to some other classes of hypergraphs, defined by conditions of similar flavour. Upper bounds on this ratio are obtained for k-colourable, strongly k-colourable and (what we call) k-partitionable hypergraphs.

Original languageEnglish
Pages (from-to)149-174
Number of pages26
JournalCombinatorica
Volume16
Issue number2
DOIs
StatePublished - 1996

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