The generalised Oberwolfach problem

Recently, much progress has been made on the general problem of decomposing a dense (usually complete) graph into a given family of sparse graphs (e.g. Hamilton cycles or trees). I will present a new result of this type: that any quasirandom dense large graph in which all degrees are equal and even can be decomposed into any given collection of two-factors (2-regular spanning subgraphs). A special case of this result reproves the Oberwolfach problem for large graphs.

This is joint work with Peter Keevash.