An infinite family of subcubic graphs with unbounded packing chromatic number

TL;DR

This paper constructs an explicit infinite family of subcubic graphs demonstrating that the packing chromatic number can be unbounded, answering a longstanding open question in graph theory.

Contribution

It introduces a new explicit family of subcubic graphs with unbounded packing chromatic number, resolving an open problem.

Findings

Unbounded packing chromatic number in subcubic graphs

Explicit construction of such graphs

Answers a key open question in the field

Abstract

Recently, Balogh, Kostochka and Liu in [Packing chromatic number of cubic graphs, Discrete Math.~341 (2018) 474--483] answered in negative the question that was posed in several earlier papers whether the packing chromatic number is bounded in the class of graphs with maximum degree $3$. In this note, we present an explicit infinite family of subcubic graphs with unbounded packing chromatic number.