Work

Bipartite Turán problems via graph gluing

Year: 2025

Type: article

Abstract: For graphs and , if we glue them by identifying a given pair of vertices and , what is the extremal number of the resulting graph ? In this paper, we study this problem and show that interestingly it is equivalent to an old question of Erdős and Simonovits on the Zarankiewicz problem. When are copies of a same bipartite graph and come from a same part, we prove that . As a corollary, we provide a short self‐contained disproof of a conjecture of Erdős, which was recently disproved by Janzer.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70243

Authors: Zichao Dong, Jun Gao, Hong Liu

Institutions: Institute for Basic Science, University of Warwick

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Institute for Basic Science

Award: G2765210714