A Proof of the Barát-Thomassen Conjecture
Julien Bensmail, Ararat Harutyunyan, Tien-Nam Le, Martin Merker, Stéphan Thomassé · arXiv (Cornell University) · 2016
The Barát-Thomassen conjecture asserts that for every tree $T$ on $m$ edges, there exists a constant $k_T$ such that every $k_T$-edge-connected graph with size divisible by $m$ can be edge-decomposed into copies of $T$. So far this conjecture has only been verified when $T$ is a path or when $T$ has diameter at most 4. Here we prove the full statement of the conjecture.