Consider a hypergraph of rank r > 2 with m edges, independence number α and edge cover number ρ. We prove the inequalityρ ≤ frac((r - 2) m + α, r - 1) .One application of this inequality is a special case of a conjecture of Aharoni and the first author extending Ryser's Conjecture to matroids.
Bibliographical noteFunding Information:
The research of the first author was supported by the National Science Foundation, under agreement No. DMS-0111298. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the view of the National Science Foundation. The research of the second author was supported by the Sacta-Rashi Foundation.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics