Oriented coloring of 2-outerplanar graphs

Louis Esperet (1) , Pascal Ochem (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A graph G is 2-outerplanar if it has a planar embedding such that the subgraph obtained by removing the vertices of the outer face is outerplanar. The oriented chromatic number of an oriented graph H is defined as the minimum order of an oriented graph H' such that H has a homomorphism to H'. In this paper, we prove that 2-outerplanar graphs are 4-degenerate. We also show that oriented 2-outerplanar graphs have a homomorphism to the Paley tournament QR67, which implies that their (strong) oriented chromatic number is at most 67.

Domaines: Autre [cs.OH]

Louis Esperet, Pascal Ochem. Oriented coloring of 2-outerplanar graphs. Information Processing Letters, 2007, 101, pp.215--219. ⟨hal-00307156⟩