Strong edge-coloring of $(3, \Delta)$-bipartite graphs

Julien Bensmail (1) , Aurélie Lagoutte (1) , Petru Valicov (2)

1 MC2 - Modèles de calcul, Complexité, Combinatoire
2 LIF - Laboratoire d'informatique Fondamentale de Marseille

A strong edge-coloring of a graph $G$ is an assignment of colors to edges such that every color class induces a matching. We here focus on bipartite graphs whose one part is of maximum degree at most $3$ and the other part is of maximum degree $\Delta$. For every such graph, we prove that a strong $4\Delta$-edge-coloring can always be obtained. Together with a result of Steger and Yu, this result confirms a conjecture of Faudree, Gyárfás, Schelp and Tuza for this class of graphs.

Mots clés: Strong edge-colouring; bipartite graphs; maximum degree

Domaines: Mathématique discrète [cs.DM]

Julien Bensmail, Aurélie Lagoutte, Petru Valicov. Strong edge-coloring of $(3, \Delta)$-bipartite graphs. Discrete Mathematics, 2016, 339 (1), ⟨10.1016/j.disc.2015.08.026⟩. ⟨hal-01080279v2⟩