Triangle-Free Subgraphs of Random Graphs

Abstract

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.

DOI: 10.1016/j.endm.2015.06.055

Cite this paper

@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} }