### 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 language | English (US) |
---|---|

Pages (from-to) | 155-160 |

Number of pages | 6 |

Journal | Combinatorica |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - 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

## Fingerprint Dive into the research topics of 'A fractional version of the Erdős-Faber-Lovász conjecture'. Together they form a unique fingerprint.

## Cite this

Kahn, J., & Seymour, P. D. (1992). A fractional version of the Erdős-Faber-Lovász conjecture.

*Combinatorica*,*12*(2), 155-160. https://doi.org/10.1007/BF01204719