Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Forbidding $K_{2,t}$ traces in triple systems (2007.01827v2)

Published 3 Jul 2020 in math.CO

Abstract: Let $H$ and $F$ be hypergraphs. We say $H$ contains $F$ as a trace if there exists some set $S \subseteq V(H)$ such that $H|S:={E\cap S: E \in E(H)}$ 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\to \infty}\lim_{n\to \infty} \frac{\mathrm{ex}(n, \mathrm{Tr}3(K{2,t}))}{t{3/2}n{3/2}} = \frac{1}{6}.$ Moreover, we show $\frac{1}{2} n{3/2} + o(n{3/2}) \leq \mathrm{ex}(n, \mathrm{Tr}_3(C_4)) \leq \frac{5}{6} n{3/2} + o(n{3/2})$.

Summary

We haven't generated a summary for this paper yet.