Constructive Packings by Linear Hypergraphs

For k-graphs F0 and H, an F0-packing of H is a family $\mathscr{F}$ of pairwise edge-disjoint copies of F0 in H. Let νF0(H) denote the maximum size |$\mathscr{F}$| of an F0-packing of H. Already in the case of graphs, computing νF0(H) is NP-hard for most fixed F0 (Dor and Tarsi [6]). In this paper,...

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Published inCombinatorics, probability & computing Vol. 22; no. 6; pp. 829 - 858
Main Authors DIZONA, JILL, NAGLE, BRENDAN
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.11.2013
Subjects
Algorithms
Secondary 05C65
Primary 05C35
05C85
Online AccessGet full text
ISSN0963-5483
1469-2163
DOI10.1017/S0963548313000291

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Summary:For k-graphs F0 and H, an F0-packing of H is a family $\mathscr{F}$ of pairwise edge-disjoint copies of F0 in H. Let νF0(H) denote the maximum size |$\mathscr{F}$| of an F0-packing of H. Already in the case of graphs, computing νF0(H) is NP-hard for most fixed F0 (Dor and Tarsi [6]). In this paper, we consider the case when F0 is a fixed linear k-graph. We establish an algorithm which, for ζ > 0 and a given k-graph H, constructs in time polynomial in |V(H)| an F0-packing of H of size at least νF0(H) − ζ |V(H)|k. Our result extends one of Haxell and Rödl, who established the analogous algorithm for graphs.
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ISSN:0963-5483
1469-2163
DOI:10.1017/S0963548313000291