Extremal problems for t-partite and t-colorable hypergraphs

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Abstract

Fix integers t ≥ r ≥ 2 and an r-uniform hypergraph F. We prove that the maximum number of edges in a t-partite r-uniform hypergraph on n vertices that contains no copy of F is ct,F (rn) + o(nr), where Ct,F can be determined by a finite computation. We explicitly define a sequence F1, F2,... of r-uniform hypergraphs, and prove that the maximum number of edges in a t-chromatic r-uniform hypergraph on n vertices containing no copy of F i is αt,r,i0(rn) + o(n r), where αt,r,i can be determined by a finite computation for each i ≥ 1. In several cases, αt,r,i is irrational. The main tool used in the proofs is the Lagrangian of a hypergraph.

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Mubayi, D., & Talbot, J. (2008). Extremal problems for t-partite and t-colorable hypergraphs. Electronic Journal of Combinatorics, 15(1 R), 1–9. https://doi.org/10.37236/750

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