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The lifting of graphs to 3-uniform hypergraphs and some applications to hypergraph Ramsey theory
Journal article   Peer reviewed

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

M. Budden, J. Hiller, J. Lambert and C. Sanford
Involve : a journal of mathematics, Vol.10(1), pp.65-76
2017
DOI: https://doi.org/10.2140/involve.2017.10.65

Abstract

Graphic methods Hypergraphs Ramsey numbers
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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