On The Entire Coloring Conjecture
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 Δ may be colored with Δ + 1 colors. In 1972, Kronk and Mitchem conjectured that the vertices, edges, and faces of a plane graph may be simultaneously colored with Δ + 4 colors. In this article, we give a simple proof that the conjecture is true if Δ ≥ 6.
Canadian Mathematical Bulletin
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Sanders, Daniel P. and Zhao, Yue, "On The Entire Coloring Conjecture" (2000). Scopus Export 2000s. 1176.