# On packing chromatic number of subcubic outerplanar graphs

## TL;DR

This paper investigates the packing chromatic number of subcubic outerplanar graphs, providing bounds based on structural properties and identifying specific classes with sharper bounds.

## Contribution

It offers new asymptotic bounds for the packing chromatic number in subcubic outerplanar graphs and refines these bounds for particular subclasses.

## Key findings

- Asymptotic bounds depending on structural properties
- Sharper bounds for specific subclasses
- Identification of classes with finite packing chromatic number

## Abstract

Although it has recently been proved that the packing chromatic number is unbounded on the class of subcubic graphs, there exists subclasses in which the packing chromatic number is finite (and small). These subclasses include subcubic trees, base-3 Sierpi{\'n}ski 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.