Antonio Girao

Monochromatic odd cycles in edge-coloured complete graphs

It is easy to see that every q-edge colouring of a complete graph on 2^q + 1 vertices contains a monochromatic odd cycle. An old question of Erdos and Graham asks for the smallest size of such monochromatic odd cycle. We will discuss a recent result (joint with Zach Hunter) in which we give the first nontrivial upper bound of the form 2^q/q^{1−o(1)}.