Document Type

Article

Publication Date

11-2009

Publication Title

European Journal of Combinatorics

Abstract

A hypergraph G=(V,E) is (k,ℓ)-sparse if no subset V⊂V spans more than k|V|−ℓ hyperedges. We characterize (k,ℓ)-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lovász, Nash-Williams, Tutte, and White and Whiteley, linking arboricity of graphs to certain counts on the number of edges. We also address the problem of finding lower-dimensional representations of sparse hypergraphs, and identify a critical behavior in terms of the sparsity parameters k and ℓ. Our constructions extend the pebble games of Lee and Streinu [A. Lee, I. Streinu, Pebble game algorithms and sparse graphs, Discrete Math. 308 (8) (2008) 1425–1437] from graphs to hypergraphs.

Volume

30

Issue

8

First Page

1944

Last Page

1964

DOI

dx.doi.org/10.1016/j.ejc.2008.12.018

ISSN

0195-6698

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