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