Planar graphs with largest injective chromatic numbers
نویسنده
چکیده
An injective coloring of graphs is a vertex coloring where two vertices receive distinct colors if they have a common neighbor. In 1977, Wegner [12] posed a conjecture on the chromatic number of squares of graphs which remains unsolved for planar graphs with maximum degrees ∆ ≥ 4. Obviously, the chromatic number of the square of a graph is at least the injective chromatic number of a graph. We present examples and constructions of planar graphs for every ∆, which have the injective chromatic number equal to the bound conjectured by Wegner.
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