A fractional version of the Erdős-Faber-Lovász conjecture
- Cite this article as:
- Kahn, J. & Seymour, P.D. Combinatorica (1992) 12: 155. doi:10.1007/BF01204719
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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.