Let G = (V,E ,F ) be a plane graph with the sets of vertices, edges, and faces V , E , and F , respectively. If one can color all elements in V ∪ E ∪ F using k colors so that any two adjacent or incident elements receive distinct colors, then G is said to be entirely k-colorable. Kronk and Mitchem [Discrete Math 5 (1973) 253-260] conjectured that every… (More)