#### Vol. 10, No. 1, 2017

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

### Mark Budden, Josh Hiller, Joshua Lambert and Chris Sanford

Vol. 10 (2017), No. 1, 65–76
##### Abstract

Given a simple graph $\Gamma$, we describe a “lifting” to a $3$-uniform hypergraph $\phi \left(\Gamma \right)$ that sends the complement of $\Gamma$ to the complement of $\phi \left(\Gamma \right)$. 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.

##### Keywords
cliques, Ramsey number, Turán graphs
##### Mathematical Subject Classification 2010
Primary: 05C65, 05C55
Secondary: 05C35