Geodesic
Facial parity edge coloring of outerplane graphs
Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 289-293.

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A facial parity edge coloring of a 2-edge-connected plane graph is such an edge coloring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same color, in addition, for each face f and each color c, either no edge or an odd number of edges incident with f is colored with c. It is known that any 2-edge-connected plane graph has a facial parity edge coloring with at most 92 colors. In this paper we prove that any 2-edge-connected outerplane graph has a facial parity edge coloring with at most 15 colors. If a 2-edge-connected outerplane graph does not contain any inner edge, then 10 colors are sufficient. Moreover, this bound is tight.
DOI : 10.26493/1855-3974.228.ee8
Keywords: plane graph, facial walk, edge coloring 
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Július Czap. Facial parity edge coloring of outerplane graphs. Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 289-293. doi : 10.26493/1855-3974.228.ee8. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.228.ee8/

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