### Abstract

For a hypergraph H let β(H) denote the minimal number of edges from H covering V(H). An edge S of H is said to represent fairly (resp. almost fairly) a partition (V_{1}, V_{2}, …, V_{m}) of for all i ≤ m. In matroids any partition of V(H) can be represented fairly by some independent set. We look for classes of hypergraphs H in which any partition of V(H) can be represented almost fairly by some edge.We show that this is true when H is the set of independent sets in a path, and conjecture that it is true when H is the set of matchings in K_{n};_{n}. We prove that partitions of E(K_{n};_{n}) into three sets can be represented almost fairly. The methods of proofs are topological.

Original language | English (US) |
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Title of host publication | A Journey through Discrete Mathematics |

Subtitle of host publication | A Tribute to Jiri Matousek |

Publisher | Springer International Publishing |

Pages | 31-58 |

Number of pages | 28 |

ISBN (Electronic) | 9783319444796 |

ISBN (Print) | 9783319444789 |

DOIs | |

State | Published - Jan 1 2017 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Mathematics(all)
- Economics, Econometrics and Finance(all)
- Business, Management and Accounting(all)

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## Cite this

*A Journey through Discrete Mathematics: A Tribute to Jiri Matousek*(pp. 31-58). Springer International Publishing. https://doi.org/10.1007/978-3-319-44479-6_2