A fractional version of the Erdős-Faber-Lovász conjecture

Jeff Kahn, P. D. Seymour

Research output: Contribution to journalArticle

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Abstract

Let H be any hypergraph in which any two edges have at most one vertex in common. We prove that one can assign non-negative real weights to the matchings of H summing to at most |V(H)|, such that for every edge the sum of the weights of the matchings containing it is at least 1. This is a fractional form of the Erdo{combining double acute accent}s-Faber-Lovász conjecture, which in effect asserts that such weights exist and can be chosen 0,1-valued. We also prove a similar fractional version of a conjecture of Larman, and a common generalization of the two.

Original languageEnglish (US)
Pages (from-to)155-160
Number of pages6
JournalCombinatorica
Volume12
Issue number2
DOIs
StatePublished - Jun 1992

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

Keywords

  • AMS subject classification code (1991): Primary: 05C65, Secondary: 05B40, 05C70

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