On the packing chromatic number of subcubic outerplanar graphs

Abstract

Although it has recently been proved that the packing chromatic number is unbounded on the class of subcubic graphs, there exist subclasses in which the packing chromatic number is finite (and small). These subclasses include subcubic trees, base-3 Sierpiński graphs and hexagonal lattices. In this paper we are interested in the packing chromatic number of subcubic outerplanar graphs. We provide asymptotic bounds depending on structural properties of the outerplanar graphs and determine sharper bounds for some classes of subcubic outerplanar graphs.