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A fractional version of the Erdős-Faber-Lovász conjecture

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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.

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Authors and Affiliations

  1. Department of Mathematics and Center of Operations Research, Rutgers University, 08903, New Brunswick, New Jersey, USA

    Jeff Kahn

  2. Bellcore 445 South Street, 07962, Morristown, New Jersey, USA

    P. D. Seymour

Authors
  1. Jeff Kahn
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  2. P. D. Seymour
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Additional information

Supported in part by NSF grant MCS 83-01867, AFOSR Grant 0271 and a Sloan Research Fellowship

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Kahn, J., Seymour, P.D. A fractional version of the Erdős-Faber-Lovász conjecture. Combinatorica 12, 155–160 (1992). https://doi.org/10.1007/BF01204719

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  • DOI: https://doi.org/10.1007/BF01204719

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