Decomposing highly connected graphs into paths of length five

Abstract

Barát and Thomassen (2006) posed the following decomposition conjecture: for each tree $T$, there exists a natural number $k_T$ such that, if $G$ is a $k_T$-edge-connected graph and $\left|E\left(G\right)\right|$ is divisible by $\left|E\left(T\right)\right|$, then $G$ admits a decomposition into copies of $T$. In a series of papers, Thomassen verified this conjecture for stars, some bistars, paths of length 3, and paths whose length is a power of 2. We verify this conjecture for paths of length 5.