2000 character limit reached
A note on Erdős-Hajnal property for graphs with VC dimension $\leq 2$ (2310.16970v1)
Published 25 Oct 2023 in math.LO and math.CO
Abstract: Using techniques in \cite{chudnovsky2023erdHos} and substitution in \cite{alon2001ramsey}, we show that there is $\epsilon>0$ such that for any graph $G$ with VC-dimension $\leq 2$, $G$ has a clique or an anti-clique of size $\geq |G|\epsilon$. We also show that Erd\H{o}s-Hajnal property of VC-dimension $1$ graphs can be proved using $\delta$-dimension technique in \cite{chernikov2018note}, and we show that when $E$ is a definable symmetric binary relation, \cite[Theorem 1.3]{chernikov2018note} can be proved without using Shelah's 2-rank..
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.