The Barat–Thomassen conjecture asserts that for every tree T on m   edges, there exists a constant kTkT such that every kTkT-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.
['Julien Bensmail', 'Ararat Harutyunyan', 'Tien Nam Le', 'Martin Merker', 'Stéphan Thomassé']
A proof of the Barát–Thomassen conjecture ☆