A SEVEN-COLOR THEOREM ON EDGE-FACE COLORING OF PLANE GRAPHS |
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| Authors: | Wang Weifan |
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| Affiliation: | Wang Weifan Department of Mathematics,Liaoning University,Shenyang 110036,China Zhang Kemin Department of Mathematics,Nanjing University,Nanjing 210093,China |
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| Abstract: | Melnikov(1975) conjectured that the edges and faces of a plane graph G can be colored with Δ(G) + 3 colors so that any two adjacent or incident elements receive distinct colors, where Δ(G) denotes the maximum degree of G. This paper proves the conjecture for the case Δ(G) ≤ 4. |
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| Keywords: | Plane graph chromatic number coloring |
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