The lifting of graphs to 3-uniform hypergraphs and some applications to hypergraph Ramsey theory

Mark Budden; Josh Hiller; Joshua Lambert; Chris Sanford

doi:10.2140/involve.2017.10.65

The lifting of graphs to 3-uniform hypergraphs and some applications to hypergraph Ramsey theory

Mark Budden, Josh Hiller, Joshua Lambert, Chris Sanford

Mathematical Sciences

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

4 Scopus citations

Abstract

Given a simple graph Γ, we describe a “lifting” to a 3-uniform hypergraph φ(Γ) that sends the complement of Γ to the complement of φ(Γ). We consider the effects of this lifting on cycles, complete subhypergraphs, and complete subhypergraphs missing a single hyperedge. Our results lead to natural lower bounds for some hypergraph Ramsey numbers.

Original language	English
Pages (from-to)	65-76
Number of pages	12
Journal	Involve
Volume	10
Issue number	1
DOIs	https://doi.org/10.2140/involve.2017.10.65
State	Published - 2017

Scopus Subject Areas

General Mathematics

Keywords

Ramsey number
Turán graphs
cliques

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10.2140/involve.2017.10.65

Cite this

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abstract = "Given a simple graph Γ, we describe a “lifting” to a 3-uniform hypergraph φ(Γ) that sends the complement of Γ to the complement of φ(Γ). We consider the effects of this lifting on cycles, complete subhypergraphs, and complete subhypergraphs missing a single hyperedge. Our results lead to natural lower bounds for some hypergraph Ramsey numbers.",

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AU - Lambert, Joshua

AU - Sanford, Chris

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AB - Given a simple graph Γ, we describe a “lifting” to a 3-uniform hypergraph φ(Γ) that sends the complement of Γ to the complement of φ(Γ). We consider the effects of this lifting on cycles, complete subhypergraphs, and complete subhypergraphs missing a single hyperedge. Our results lead to natural lower bounds for some hypergraph Ramsey numbers.

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KW - Turán graphs

KW - cliques

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The lifting of graphs to 3-uniform hypergraphs and some applications to hypergraph Ramsey theory

Abstract

Scopus Subject Areas

Keywords

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