Research reveals efficient coloring methods for vertices in planar graphs, enhancing structural understanding.
The vertex set of any planar graph of minimum degree at least 3 can be colored in two colors so that every vertex has a neighbor of each color. If the graph is a planar triangulation, the coloring can be chosen such that every vertex has a neighbor of its own color and at least two neighbors of the opposite color.
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Rotenberg et al. (2026) studied this question.
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