Decompositions of highly connected graphs into paths of any given length

Abstract

We study the decomposition conjecture posed by Barát and Thomassen (2006), which states that, for each tree T, there exists a natural number kT such that, if G is a kT-edge-connected graph and |E(T)| divides |E(G)|, then G admits a partition of its edge set into classes each of which induces a copy of T. In a series of papers, starting in 2008, Thomassen has verified this conjecture for stars, some bistars, paths of length 3, and paths whose length is a power of 2. In 2014, we verified this conjecture for paths of length 5. In this paper we verify this conjecture for paths of any given length.