Bounds and complexity results for strong edge colouring of subcubic graphs

Hervé Hocquard (1) , Pascal Ochem (2) , Petru Valicov (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LRI - Laboratoire de Recherche en Informatique

A strong edge colouring of a graph $G$ is a proper edge colouring such that every path of length 3 uses three colours. In this paper, we give some upper bounds for the minimum number of colours in a strong edge colouring of subcubic graphs as a function of the maximum average degree. We also prove the NP-completeness of the strong edge $k$-colouring problem for some restricted classes of subcubic planar graphs when $k=4,5,6$.

Domaines: Mathématique discrète [cs.DM]; Complexité [cs.CC]

Hervé Hocquard, Pascal Ochem, Petru Valicov. Bounds and complexity results for strong edge colouring of subcubic graphs. EuroComb'11, Aug 2011, Budapest, France. A paraitre. ⟨hal-00592130⟩