Work

Equivalence between Erdős–Hajnal and polynomial Rödl and Nikiforov conjectures

Year: 2026

Type: article

Abstract: It is well‐known that polynomial versions of theorems of Rödl and Nikiforov, as conjectured by Fox and Sudakov and Nguyen, Scott and Seymour imply the classical Erdős–Hajnal conjecture. In this note, we prove that these three conjectures are in fact equivalent, extending several previous particular results in this direction by Fox, Nguyen, Scott, and Seymour; Nguyen, Scott, and Seymour; and Gishboliner and Shapira. We deduce that the family of string graphs satisfies the polynomial Rödl conjecture. We also derive analogous results for hypergraphs, tournaments, ordered graphs, and colored graphs.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70493

Authors: Matija Bucić, Jacob Fox, Huy Tuan Pham

Institutions: University of Vienna, Princeton University, Stanford University, University of Chicago

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: $3,930

Funder: National Science Foundation