  A common problem in graph colouring seeks to decompose the edge set of a
given graph into few similar and simple subgraphs, under certain divisibility
conditions. In 1987 Wormald conjectured that the edges of every cubic graph on
$4n$ vertices can be partitioned into two isomorphic linear forests. We prove
this conjecture for large connected cubic graphs. Our proof uses a wide range
of probabilistic tools in conjunction with intricate structural analysis, and
introduces a variety of local recolouring techniques.
