. Coloring problems include some of the most classical combinatorial problems (such as map coloring problems or edge coloring of cubic graphs). But the area is alive and well beeing refreshed by a constant stream of new problems and solutions of old ones. In this paper we complement this by a survey of four particular problems which are all related to the notion of a homomorphism. This forms one of the most recent approaches to coloring problems. Keywords. Chromatic number, Planar graphs, Homomorphism, Gap, Density, Quasiordering, Oriented chromatic number, Game chromatic number.
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