Hypergraph Independent Sets
Document Type
Article
Publication Date
1-1-2013
Abstract
The study of extremal problems related to independent sets in hypergraphs is a problem that has generated much interest. There are a variety of types of independent sets in hypergraphs depending on the number of vertices from an independent set allowed in an edge. We say that a subset of vertices is j-independent if its intersection with any edge has size strictly less than j. The Kruskal-Katona theorem implies that in an r-uniform hypergraph with a fixed size and order, the hypergraph with the most r-independent sets is the lexicographic hypergraph. In this paper, we use a hypergraph regularity lemma, along with a technique developed by Loh, Pikhurko and Sudakov, to give an asymptotically best possible upper bound on the number of j-independent sets in an r-uniform hypergraph.
DOI
10.1017/S0963548312000454
MSU Digital Commons Citation
Cutler, Jonathan and Radcliffe, A. J., "Hypergraph Independent Sets" (2013). Department of Mathematics Facuty Scholarship and Creative Works. 87.
https://digitalcommons.montclair.edu/mathsci-facpubs/87
