Covering a hypergraph of subgraphs

Noga Alon

doi:10.1016/S0012-365X(02)00427-2

Covering a hypergraph of subgraphs

Noga Alon^*

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Conference article › peer-review

13 Scopus citations

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 language	English
Pages (from-to)	249-254
Number of pages	6
Journal	Discrete Mathematics
Volume	257
Issue number	2-3
DOIs	https://doi.org/10.1016/S0012-365X(02)00427-2
State	Published - 28 Nov 2002
Event	Kleitman and Combinatorics: A Celebration - Cambridge, MA, United States Duration: 16 Aug 1990 → 18 Aug 1990

Funding

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

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10.1016/S0012-365X(02)00427-2

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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.",

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N2 - 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.

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T2 - Kleitman and Combinatorics: A Celebration

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Covering a hypergraph of subgraphs

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