Geodesic
Unique-Maximum Coloring Of Plane Graphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 95-102

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A unique-maximum k-coloring with respect to faces of a plane graph G is a coloring with colors 1, . . ., k so that, for each face of G, the maximum color occurs exactly once on the vertices of α. We prove that any plane graph is unique-maximum 3-colorable and has a proper unique-maximum coloring with 6 colors.
Keywords: plane graph, weak-parity coloring, unique-maximum coloring 
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Fabrici, Igor; Göring, Frank. Unique-Maximum Coloring Of Plane Graphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 95-102. http://geodesic.mathdoc.fr/item/DMGT_2016_36_1_a6/