Katherine Staden

Ringel's conjecture on tree-packing

When can (the edge-set of) a graph $G$ be decomposed into copies of a given graph $H$? This question goes all the way back to Euler; despite this, the setting where the number of vertices in $G$ and $H$ are comparable is not yet well-understood. I will talk about the resolution of a conjecture of Ringel from 1963 where $G$ is the complete graph on $2n+1$ vertices and $H$ is any given tree with $n$ edges. This is joint work with Peter Keevash; the conjecture was independently resolved by Montgomery, Pokrovskiy and Sudakov.