coloring, square, subcubic, planar graph, discharging, computational proof
Discrete Mathematics and Combinatorics
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.
Stephen Hartke, Sogol Jahanbekam, and Brent Thomas. "The chromatic number of the square of subcubic planar graphs" Faculty Publications (2016).
This work is also available on Arxiv.org at this link.