We show that if G is a simple triangle-free graph with n≥3 vertices, without a perfect matching, and having a minimum degree at least 2n−1, then G is isomorphic either to C5 or to K2n−1,2n+1.
@article{arxiv.1101.3188,
title = {A note on triangle-free graphs},
author = {Vahan V. Mkrtchyan and Petros A. Petrosyan},
journal= {arXiv preprint arXiv:1101.3188},
year = {2015}
}