Edge-partitioning a graph into paths: beyond the Barát-Thomassen conjecture

The Barát-Thomassen conjecture asserts that there is a function f such that for every fixed tree T with t edges, every graph which is f(t)edge-connected with its number of edges divisible by t has a partition of its edges into copies of T . This has been proved in the case of paths of length 2 by Thomassen [14], and recently shown to be true for all paths by Botler, Mota, Oshiro and Wakabayashi [2]. Our goal in this paper is to propose an alternative proof of the path case with a weaker hypothesis: Namely, we prove that there is a function f such that every 24-edge-connected graph with minimum degree f(t) has an edge-partition into paths of length t whenever t divides the number of edges. We also show that 24 can be dropped to 4 when the graph is eulerian.