The chromatic number of the square of subcubic planar graphs

TL;DR

This paper proves Wegner's 1977 conjecture that the square of any subcubic planar graph can be colored with at most 7 colors, using discharging and computational methods.

Contribution

It provides a complete proof of Wegner's conjecture for subcubic planar graphs, combining discharging and computational verification.

Findings

Confirmed Wegner's conjecture for subcubic planar graphs

Established that the square of such graphs is 7-colorable

Used computational techniques to verify reducible configurations

Abstract

Wegner conjectured in 1977 that the square of every planar graph with maximum degree at most $3$ is $7$-colorable. We prove this conjecture using the discharging method and computational techniques to verify reducible configurations.