Combinatorica

, Volume 12, Issue 2, pp 155–160 | Cite as

A fractional version of the Erdős-Faber-Lovász conjecture

  • Jeff Kahn
  • P. D. Seymour
Article

Abstract

LetH 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 ofH 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 Erdős-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.

AMS subject classification code (1991)

Primary: 05 C 65 Secondary: 05 B 40 05 C 70 

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Copyright information

© Akadémiai Kiadó 1992

Authors and Affiliations

  • Jeff Kahn
    • 1
  • P. D. Seymour
    • 2
  1. 1.Department of Mathematics and Center of Operations ResearchRutgers UniversityNew BrunswickUSA
  2. 2.MorristownUSA

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