On isomorphic linear partitions in cubic graphs

@article{Fouquet2009OnIL,
  title={On isomorphic linear partitions in cubic graphs},
  author={Jean-Luc Fouquet and Henri Thuillier and Jean-Marie Vanherpe and A. Pawel Wojda},
  journal={Discrete Mathematics},
  year={2009},
  volume={309},
  pages={6425-6433}
}
A linear forest is a graph that connected components are chordless paths. A linear partition of a graph G is a partition of its edge set into linear forests and la(G) is the minimum number of linear forests in a linear partition. It is well known that la(G) = 2 when G is a cubic graph and Wormald [17] conjectured that if |V (G)| ≡ 0 (mod 4), then it is always possible to find a linear partition in two isomorphic linear forests. We give here some new results concerning this conjecture. 

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