Highly Influential

5 Excerpts

- Published 2015 in Electronic Notes in Discrete Mathematics

The Andrásfai–Erdős–Sós Theorem [2] states that all triangle-free graphs on n vertices with minimum degree strictly greater than 2n/5 are bipartite. Thomassen [11] proved that when the minimum degree condition is relaxed to ( 3 + ε)n, the result is still guaranteed to be rε-partite, where rε does not depend on n. We prove best possible random graph analogues of these theorems.

@article{Allen2015TriangleFreeSO,
title={Triangle-Free Subgraphs of Random Graphs},
author={Peter Allen and Julia B{\"{o}ttcher and Barnaby Roberts and Yoshiharu Kohayakawa},
journal={Electronic Notes in Discrete Mathematics},
year={2015},
volume={49},
pages={393-397}
}