Year: 2026
Type: article
Abstract: ABSTRACT Solving a long standing conjecture of Erdős and Simonovits, Brandt and Thomassé proved that the chromatic number of each triangle‐free graph such that is at most four. In fact, they showed the much stronger result that every maximal triangle‐free graph satisfying this minimum degree condition is a blow‐up of either an Andrásfai or a Vega graph. Here we establish the same structural conclusion on under the weaker assumption that for every sequence of vertices has a subsequence of length with a common neighbour. In forthcoming work this will be used to solve an old problem of Andrásfai in Ramsey‐Turán theory.
Source: Journal of Graph Theory
DOI: 10.1002/jgt.70117
Authors: Tomasz Łuczak, Joanna Polcyn, Christian Reiher
Institutions: Adam Mickiewicz University in Poznań, Universität Hamburg
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Narodowym Centrum Nauki
Award: G6849557733
OpenAlex ID: W7212059237