Rational exponents for hypergraph Turan problems

2016/07/20 by Matthew Fitch, Fitch, Matthew · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1607.05788

22 pages, 3 figures

arxiv created 2017/06/15 · arxiv updated 2017/06/16

Abstract

Given a family of k-hypergraphs F, ex(n,F) is the maximum number of edges a k-hypergraph can have, knowing that said hypergraph has n vertices but contains no copy of any hypergraph from F as a subgraph. We prove that for every rational r between 0 and k-1, there exists some finite family F of k-hypergraphs for which ex(n,F)=Θ(n^k-r).

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• Rational Exponents for General Graphs

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