On oriented arc-coloring of subcubic graphs

Alexandre Pinlou (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A homomorphism from an oriented graph G to an oriented graph H is a mapping from the set of vertices of G to the set of vertices of H such that $\phi$(u)$\phi$(v) is an arc in H whenever is uv an arc in G. The oriented chromatic index of an oriented graph G is the minimum number of vertices in an oriented graph H such that there exists a homomorphism from the line digraph LD(G) of G to H (Recall that LD(G) is given by V (LD(G)) = A(G) and A(LD(G). We prove that every oriented subcubic graph has oriented chromatic index at most 7 and construct a subcubic graph with oriented chromatic index 6.

Mots clés: Graph coloring; oriented graph coloring; arc-coloring; subcubic graphs; subcubic graphs.

Domaines: Autre [cs.OH]

Alexandre Pinlou. On oriented arc-coloring of subcubic graphs. The Electronic Journal of Combinatorics, 2006, 13, pp.131. ⟨hal-00307094⟩