## Abstract

For a simplicial complex C denote by β(C) the minimal number of edges from C needed to cover the ground set. If C is a matroid then for every partition A_{1},…,A_{m} of the ground set there exists a set S∈C meeting each A_{i} in at least [Formula presented] elements. We conjecture a slightly weaker statement for the intersection of two matroids: if D=P∩Q, where P, Q are matroids on the same ground set V, and β(P), β(Q)≤k, then for every partition A_{1},…,A_{m} of the ground set there exists a set S∈D meeting each A_{i} in at least [Formula presented]|A_{i}|−1 elements. We prove that when m=2 there is a set meeting each A_{i} in at least ([Formula presented]−[Formula presented])|A_{i}|−1 elements.

Original language | English |
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Pages (from-to) | 5-11 |

Number of pages | 7 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 61 |

DOIs | |

State | Published - Aug 2017 |

### Bibliographical note

Publisher Copyright:© 2017 Elsevier B.V.

## Keywords

- edge covering number
- edge-cover
- fair representation
- matroid

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics