Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
133 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

Random Turán Problems for $K_{s,t}$ Expansions (2412.09367v1)

Published 12 Dec 2024 in math.CO and math.PR

Abstract: Let $K_{s,t}{(r)}$ denote the $r$-uniform hypergraph obtained from the graph $K_{s,t}$ by inserting $r-2$ new vertices inside each edge of $K_{s,t}$. We prove essentially tight bounds on the size of a largest $K_{s,t}{(r)}$-subgraph of the random $r$-uniform hypergraph $G_{n,p}r$ whenever $r\ge 2s/3+2$, giving the first random Tur\'an results for expansions that go beyond a natural "tight-tree barrier." In addition to this, our methods yield optimal supersaturation results for $K_{s,t}{(3)}$ for sufficiently dense host hypergraphs, which may be of independent interest.

Summary

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

X Twitter Logo Streamline Icon: https://streamlinehq.com