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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
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Abstract |
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Given a simple graph , we describe a “lifting” to a -uniform hypergraph that sends the complement of to the complement of . 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
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Mathematical Subject Classification 2010
Primary: 05C65, 05C55
Secondary: 05C35
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Milestones
Received: 16 August 2015
Revised: 2 December 2015
Accepted: 13 December 2015
Published: 11 October 2016
Communicated by Joshua Cooper
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Authors |
| Mark Budden | |
| Department of Mathematics and
Computer Science Western Carolina University Cullowhee, NC 28723 United States |
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| Josh Hiller | |
| Department of Mathematics PO Box 118105 University of Florida Gainesville, FL 32611 United States |
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| Joshua Lambert | |
| Department of Mathematics Armstrong Atlantic State University 11935 Abercorn Street Savannah, GA 31419 United States |
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| Chris Sanford | |
| Department of Mathematics Syracuse University Syracuse, NY 13244 United States |
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