Cycles as edge intersection hypergraphs

Martin Sonntag; Hanns-Martin Teichert

Cycles as edge intersection hypergraphs

Martin Sonntag, Hanns-Martin Teichert

Institute of Mathematics

Technische Universität Bergakademie Freiberg

Abstract

If H = (V,E) is a hypergraph, its edge intersection hypergraph EI(H) = (V,EEI) hastheedgesetEEI={e1∩e2|e1,e2∈E∧e1̸=e2 ∧|e1∩e2|≥2}.Pickingupaproblem from [7], for n ≥ 24 we prove that there is a 3-regular (and - if n is even - 6-uniform) hypergraph H = (V,E) with ⌈n⌉ hyperedges and EI(H) = Cn.

Original language	English
Publication status	Published - 2019

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https://arxiv.org/abs/1902.00396

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title = "Cycles as edge intersection hypergraphs",

abstract = "If H = (V,E) is a hypergraph, its edge intersection hypergraph EI(H) = (V,EEI) hastheedgesetEEI={e1∩e2|e1,e2∈E∧e1̸=e2 ∧|e1∩e2|≥2}.Pickingupaproblem from [7], for n ≥ 24 we prove that there is a 3-regular (and - if n is even - 6-uniform) hypergraph H = (V,E) with ⌈n⌉ hyperedges and EI(H) = Cn.",

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AU - Teichert, Hanns-Martin

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N2 - If H = (V,E) is a hypergraph, its edge intersection hypergraph EI(H) = (V,EEI) hastheedgesetEEI={e1∩e2|e1,e2∈E∧e1̸=e2 ∧|e1∩e2|≥2}.Pickingupaproblem from [7], for n ≥ 24 we prove that there is a 3-regular (and - if n is even - 6-uniform) hypergraph H = (V,E) with ⌈n⌉ hyperedges and EI(H) = Cn.

AB - If H = (V,E) is a hypergraph, its edge intersection hypergraph EI(H) = (V,EEI) hastheedgesetEEI={e1∩e2|e1,e2∈E∧e1̸=e2 ∧|e1∩e2|≥2}.Pickingupaproblem from [7], for n ≥ 24 we prove that there is a 3-regular (and - if n is even - 6-uniform) hypergraph H = (V,E) with ⌈n⌉ hyperedges and EI(H) = Cn.

M3 - Other

ER -

Cycles as edge intersection hypergraphs

Abstract

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