On strong edge-colouring of subcubic graphs

Hervé Hocquard (1) , Mickael Montassier (1) , André Raspaud (1) , Petru Valicov (1)

1 LaBRI - Laboratoire Bordelais 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 different colours. In this paper we improve some previous results on the strong edge-colouring of subcubic graphs by showing that every subcubic graph with maximum average degree strictly less than 7/3 (resp. 5/2, 8/3, 20/7) can be strongly edge-coloured with six (resp. seven, eight, nine) colours. These upper bounds are optimal except the one of 8/3. Also, we prove that every subcubic planar graph without 4-cycles and 5-cycles can be strongly edge-coloured with nine colours.

Mots clés: Strong edge-colouring; subcubic graphs; planar graphs; maximum average degree

Domaines: Mathématique discrète [cs.DM]

Hervé Hocquard, Mickael Montassier, André Raspaud, Petru Valicov. On strong edge-colouring of subcubic graphs. Discrete Applied Mathematics, 2013, 161 (16-17), pp.2467-2479. ⟨10.1016/j.dam.2013.05.021⟩. ⟨hal-00686021v2⟩