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 A1,…,Am of the ground set there exists a set S∈C meeting each Ai 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 A1,…,Am of the ground set there exists a set S∈D meeting each Ai in at least [Formula presented]|Ai|−1 elements. We prove that when m=2 there is a set meeting each Ai in at least ([Formula presented]−[Formula presented])|Ai|−1 elements.
Bibliographical notePublisher Copyright:
© 2017 Elsevier B.V.
- edge covering number
- fair representation
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics