Elsevier

Discrete Mathematics

Volume 308, Issue 12, 28 June 2008, Pages 2649-2654
Discrete Mathematics

Note
A note on the edge cover number and independence number in hypergraphs

https://doi.org/10.1016/j.disc.2007.05.006Get rights and content
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Abstract

Consider a hypergraph of rank r>2 with m edges, independence number α and edge cover number ρ. We prove the inequalityρ(r-2)m+αr-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.

Keywords

Hypergraphs
Matching
Covering
Independence

Cited by (0)

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.