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- W1507616401 abstract "Let be a plane graph with the sets of vertices, edges, and faces V, E, and F, respectively. If one can color all elements in 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 plane graph with maximum degree Δ is entirely -colorable. This conjecture has now been settled in Wang and Zhu (J Combin Theory Ser B 101 (2011) 490–501), where the authors asked: is every simple plane graph entirely -colorable? In this article, we prove that every simple plane graph with is entirely -colorable, and conjecture that every simple plane graph, except the tetrahedron, is entirely -colorable." @default.
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- W1507616401 date "2012-07-30" @default.
- W1507616401 modified "2023-09-27" @default.
- W1507616401 title "Plane Graphs with Maximum Degree Δ≥8 Are Entirely (Δ+3)-Colorable" @default.
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- W1507616401 doi "https://doi.org/10.1002/jgt.21676" @default.
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