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

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.

cliques, Ramsey number, Turán graphs
Mathematical Subject Classification 2010
Primary: 05C65, 05C55
Secondary: 05C35
Received: 16 August 2015
Revised: 2 December 2015
Accepted: 13 December 2015
Published: 11 October 2016

Communicated by Joshua Cooper
Mark Budden
Department of Mathematics and Computer Science
Western Carolina University
Cullowhee, NC 28723
United States
Josh Hiller
Department of Mathematics
PO Box 118105
University of Florida
Gainesville, FL 32611
United States
Joshua Lambert
Department of Mathematics
Armstrong Atlantic State University
11935 Abercorn Street
Savannah, GA 31419
United States
Chris Sanford
Department of Mathematics
Syracuse University
Syracuse, NY 13244
United States