Geodesic
A Survey on the Cyclic Coloring and its Relaxations
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 5-38

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A cyclic coloring of a plane graph is a vertex coloring such that any two vertices incident with the same face receive distinct colors. This type of coloring was introduced more than fifty years ago, and a lot of research in chromatic graph theory was sparked by it. This paper is a survey on the state of the art concerning the cyclic coloring and relaxations of this graph invariant.
Keywords: plane graph, edge coloring, vertex coloring 
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Czap, Július; Horňák, Mirko; Jendroľ, Stanislav. A Survey on the Cyclic Coloring and its Relaxations. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 1, pp. 5-38. http://geodesic.mathdoc.fr/item/DMGT_2021_41_1_a0/