Tutte Colloquium - Richard Lang

Title: Monochromatic cycle partitions

Abstract:

A classic result of Erdős, Gyárfás, and Pyber states that the vertex set of every complete graph, whose edges have been coloured with r colours, can be covered by r² log r disjoint monochromatic cycles.The search for such monochromatic cycle partitions has received a lot of attention in the past years and many generalizations have been developed.

In this talk, I will give an introduction to the topic, the methods used to tackle its problems, and discuss a recent strengthening of the above theorem to graphs of minimum degree density at least 1/2+o(1).