0 KB170 KB11 KB200820252012Czap, Júliusštevilka:2letnik:5str. 289-293COBISSID:16276825ISSN:1855-3966URN:URN:NBN:SI:doc-CSTHJQJPenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneabarvanje povezavedge coloringfacial walkgraph theoryplane graphravninski grafteorija grafovFacial parity edge coloring of outerplane graphs|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 tightTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije