School of Mathematics, Birmingham University, UK

_{1},…, T

_{n}is a sequence of bounded degree trees so that T

_{i}has i vertices, then K

_{n}has a decomposition into T

_{1},…, T

_{n}. This shows that the tree packing conjecture of Gyárfás and Lehel from 1976 holds for all bounded degree trees.

We deduce this result from a more general theorem, which yields decompositions of dense quasi-random graphs into suitable families of bounded degree graphs.

In this talk, we discuss the ideas used in the proof.

This is joint work with Felix Joos, Daniela Kühn and Deryk Osthus.