Looms

Ron Aharoni; Eli Berger; Joseph Briggs; He Guo; Shira Zerbib

doi:10.1016/j.disc.2024.114181

Looms

Ron Aharoni, Eli Berger, Joseph Briggs, He Guo, Shira Zerbib

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A pair (A,B) of hypergraphs is called orthogonal if |a∩b|=1 for every pair of edges a∈A,b∈B. An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appear naturally in the context of a conjecture of Gyárfás and Lehel on the covering number of cross-intersecting hypergraphs. We study their properties and ways of construction, and prove special cases of a conjecture that if true would imply the Gyárfás–Lehel conjecture.

Original language	English
Article number	114181
Journal	Discrete Mathematics
Volume	347
Issue number	12
DOIs	https://doi.org/10.1016/j.disc.2024.114181
State	Published - Dec 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier B.V.

Keywords

Covering numbers of hypergraphs
Fractional matchings
Intersecting hypergraphs
Matchings in hypergraphs
r-partite hypergraphs

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2024.114181

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abstract = "A pair (A,B) of hypergraphs is called orthogonal if |a∩b|=1 for every pair of edges a∈A,b∈B. An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appear naturally in the context of a conjecture of Gy{\'a}rf{\'a}s and Lehel on the covering number of cross-intersecting hypergraphs. We study their properties and ways of construction, and prove special cases of a conjecture that if true would imply the Gy{\'a}rf{\'a}s–Lehel conjecture.",

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AU - Berger, Eli

AU - Briggs, Joseph

AU - Guo, He

AU - Zerbib, Shira

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AB - A pair (A,B) of hypergraphs is called orthogonal if |a∩b|=1 for every pair of edges a∈A,b∈B. An orthogonal pair of hypergraphs is called a loom if each of its two members is the set of minimum covers of the other. Looms appear naturally in the context of a conjecture of Gyárfás and Lehel on the covering number of cross-intersecting hypergraphs. We study their properties and ways of construction, and prove special cases of a conjecture that if true would imply the Gyárfás–Lehel conjecture.

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KW - Fractional matchings

KW - Intersecting hypergraphs

KW - Matchings in hypergraphs

KW - r-partite hypergraphs

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SN - 0012-365X

VL - 347

JO - Discrete Mathematics

JF - Discrete Mathematics

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ER -

Looms

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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