On isomorphic linear partitions in cubic graphs

Jean-Luc Fouquet (1) , Henri Thuillier (1) , Jean-Marie Vanherpe (1) , Adam Pawel Wojda (2)

1 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans
2 AGH UST - AGH University of Science and Technology [Krakow, PL]

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 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.

Mots clés: cubic graphs; linear-arboricity

Domaines: Mathématique discrète [cs.DM]

Jean-Luc Fouquet, Henri Thuillier, Jean-Marie Vanherpe, Adam Pawel Wojda. On isomorphic linear partitions in cubic graphs. Discrete Mathematics, 2009, 309 (22), pp.6425-6433. ⟨hal-00144338⟩