Work

A Note on the Strong Erdős–hajnal Property for Graphs With Bounded Vc-minimal Complexity

Year: 2024

Type: article

Abstract: Inspired by Adler’s idea on VC minimal theories [1], we introduce VC-minimal complexity. We show that for any $N\in \mathbb {N}^{>0}$ , there is $k_N>0$ such that for any finite bipartite graph $(X,Y;E)$ with VC-minimal complexity $< N$ , there exist $X'\subseteq X$ , $Y'\subseteq Y$ with $|X'|\geq k_N |X|$ , $|Y'|\geq k_N |Y|$ such that $X'\times Y' \subseteq E$ or $X'\times Y'\cap E=\emptyset $ .

Source: Journal of Symbolic Logic

DOI: 10.1017/jsl.2024.56

Author: YAYI FU

Institution: University of Notre Dame

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,450

Funder: National Science Foundation