Geodesic
On the Entire Coloring Conjecture
Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 108-114

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The Four Color Theorem says that the faces (or vertices) of a plane graph may be colored with four colors. Vizing’s Theorem says that the edges of a graph with maximum degree $\Delta$ may be colored with $\Delta \,+\,1$ colors. In 1972, Kronk and Mitchem conjectured that the vertices, edges, and faces of a plane graph may be simultaneously colored with $\Delta \,+\,4$ colors. In this article, we give a simple proof that the conjecture is true if $\Delta \,\ge \,6$ .
DOI : 10.4153/CMB-2000-017-7
Mots-clés : 05C15, 05C10 
Sanders, Daniel P.; Zhao, Yue. On the Entire Coloring Conjecture. Canadian mathematical bulletin, Tome 43 (2000) no. 1, pp. 108-114. doi: 10.4153/CMB-2000-017-7
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     doi = {10.4153/CMB-2000-017-7},
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