On facial unique-maximum (edge-)coloring

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2018-03-11
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Andova, Vesna
Luzar, Borut
Skrekovski, Riste
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Lidicky, Bernard
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Mathematics
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Abstract

A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face α the maximal color appears exactly once on the vertices of α. If the coloring is required to be proper, then the upper bound for the minimal number of colors required for such a coloring is set to 5. Fabrici and Göring [5] even con- jectured that 4 colors always suffice. Confi the conjecture would hence give a considerable strengthening of the Four Color Theorem. In this paper, we prove that the conjecture holds for subcubic plane graphs, outerplane graphs and plane quadrangulations. Additionally, we consider the facial edge-coloring analogue of the aforementioned coloring and prove that every 2-connected plane graph admits such a coloring with at most 4 colors.

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This is a manuscript of an article pulblished as Andova, Vesna, Bernard Lidický, Borut Lužar, and Riste Škrekovski. "On facial unique-maximum (edge-) coloring." Discrete Applied Mathematics 237 (2018): 26-32. doi: 10.1016/j.dam.2017.11.024. Posted with permission.

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Sun Jan 01 00:00:00 UTC 2017
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