Graphs with large minimum degree and no small odd cycles are $3$-colourable

Julia Böttcher, Nóra Frankl, Domenico Mergoni Cecchelli +2

Answering a question by Letzter and Snyder, we prove that for large enough $k$ any $n$-vertex graph $G$ with minimum degree at least $\frac{1}{2k-1}n$ and without odd cycles of len…