Constructing r-Uniform Hypergraphs with Restricted Clique Numbers

Abstract

Ramsey theory has posed many interesting questions for graph theorists that have yet to be solved.  Many different methods have been used to find Ramsey numbers, though very few are actually known.  Because of this, more mathematical tools are needed to prove exact values of Ramsey numbers and their generalizations.  Budden, Hiller, Lambert, and Sanford have created a lifting from graphs to 3-uniform hypergraphs that has shown promise in extending known Ramsey results to hypergraphs.  This paper will consider another analogous lifting for $r$-uniform hypergraphs and investigate the lifting of Turan graphs.