A proof of the Barat Thomassen conjecture

摘要

The Barat Thomassen conjecture asserts that for every tree T on m edges, there exists a constant k(T) such that every kT-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. (C) 2016 Elsevier Inc. All rights reserved.