Covering a hypergraph of subgraphs

Noga Alon*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

Let G be a tree and let ℋ be a collection of subgraphs of G, each having at most d connected components. Let v(ℋ) denote the maximum number of members of ℋ no two of which share a common vertex, and let τ(ℋ) denote the minimum cardinality of a set of vertices of G that intersects all members of ℋ. It is shown that τ(ℋ) ≤ 2d2v(ℋ). A similar, more general result is proved replacing the assumption that G is a tree by the assumption that it has a bounded tree-width. These improve and extend results of various researchers.

Original languageEnglish
Pages (from-to)249-254
Number of pages6
JournalDiscrete Mathematics
Volume257
Issue number2-3
DOIs
StatePublished - 28 Nov 2002
EventKleitman and Combinatorics: A Celebration - Cambridge, MA, United States
Duration: 16 Aug 199018 Aug 1990

Funding

FundersFunder number
Hermann Minkowski Minerva Center for Geometry
Bloom's Syndrome Foundation
Israel Science Foundation
Tel Aviv University

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