Forbidding K_2,t traces in triple systems

2020/07/03 by Luo, Ruth, Spiro, Sam
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.01827

Abstract

Let H and F be hypergraphs. We say H contains F as a trace if there exists some set S ⊆ V(H) such that H|_S:=\E∩ S: E ∈ E(H)\ contains a subhypergraph isomorphic to F. In this paper we give an upper bound on the number of edges in a 3-uniform hypergraph that does not contain K_2,t as a trace when t is large. In particular, we show that lim_{t→ ∞}lim_{n→ ∞} \fracex(n, Tr₃(K_2,t))t^3/2n^3/2 = (1)/(6). Moreover, we show (1)/(2) n^3/2 + o(n^3/2) ≤ ex(n, Tr₃(C₄)) ≤ (5)/(6) n^3/2 + o(n^3/2).

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