On r-uniform linear hypergraphs with no Berge-K_2,t

2016/09/12 by Timmons, Craig · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.03401

Abstract

Let F be an r-uniform hypergraph and G be a multigraph. The hypergraph F is a Berge-G if there is a bijection f: E(G) → E( F ) such that e ⊆ f(e) for each e ∈ E(G). Given a family of multigraphs G, a hypergraph H is said to be G-free if for each G ∈ G, H does not contain a subhypergraph that is isomorphic to a Berge-G. We prove bounds on the maximum number of edges in an r-uniform linear hypergraph that is K_2,t-free. We also determine an asymptotic formula for the maximum number of edges in a linear 3-uniform 3-partite hypergraph that is \C₃ , K_2,3 \-free.

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