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arxiv: 1604.06504 · v1 · pith:OWF6MBZJnew · submitted 2016-04-21 · 🧮 math.CO

The chromatic number of the square of subcubic planar graphs

classification 🧮 math.CO
keywords planarsquarechromaticcolorablecomputationalconfigurationsconjectureconjectured
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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.

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Cited by 2 Pith papers

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  1. Subcubic $K_4$-minor-free graphs without crumby colorings

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    Counterexamples disprove the conjecture that every K4-minor-free graph has a crumby coloring, with the smallest connected one having 18 vertices and a 2-connected one having 40 vertices.

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    math.CO 2022-10 unverdicted

    This is a survey compiling results on strong edge-coloring and related coloring problems for squares of graphs in planar and sparse classes.