Barat 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 | E ( G ) | is divisible by | E ( T ) | , 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.
