Year: 2026
Type: preprint
Abstract: For a zero-one matrix $P$, let $\operatorname{Ex}(n,P)$ denote the maximum number of ones in an $n\times n$ zero-one matrix avoiding $P$. We prove that $$\operatorname{Ex}(n,P) \leq n^{1+O_P(1/\log\log n)}$$ for every acyclic $P$, settling the weak form of the Pach-Tardos conjecture.
Source: arXiv (Cornell University)
Authors: Gishboliner, Lior, Li, Xiangyu
Institution: University of Toronto
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213580501