On packing chromatic number of subcubic outerplanar graphs

Nicolas Gastineau (1) , Přemysl Holub (2) , Olivier Togni (3)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 kma
3 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

The question of whether subcubic graphs have finite packing chromatic number or not is still open although positive responses are known for some subclasses, including subcubic trees, base-3 Sierpiski graphs and hexagonal lattices. In this paper, we answer positively to the question for some subcubic outerplanar graphs. We provide asymptotic bounds depending on structural properties of the weak dual of the outerplanar graphs and determine sharper bounds on some classes of subcubic outerplanar graphs.

Mots clés: packing colouring; packing chromatic number; outerplanar graphs; subcubic; graphs; AMS Subject Classification:

Domaines: Mathématique discrète [cs.DM]

Nicolas Gastineau, Přemysl Holub, Olivier Togni. On packing chromatic number of subcubic outerplanar graphs. 2017. ⟨hal-01489300v1⟩