0 KB435 KB37 KB200820252011Czap, JúliusJendrol, StanislavKardoš, Františekštevilka:2letnik:4str. 255-268COBISSID:16267097ISSN:1855-3966URN:URN:NBN:SI:doc-FJ9ESYSGenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneabarvanje povezavedge colouringfacial walkgraph theoryplane graphsravninski grafiteorija grafovFacial parity edge colouring|A facial parity edge colouring of a connected bridgeless plane graph is an edge colouring in which no two face-adjacent edges (consecutive edges of a facial walk of some face) receive the same colour, in addition, for each face $\alpha$ and each colour $c$, either no edge or an odd number of edges incident with $\alpha$ is coloured with $c$. From Vizing's theorem it follows that every 3-connected plane graph has a such colouring with at most $\Delta^\ast + 1$ colours, where $\Delta^\ast$ is the size of the largest face. In this paper we prove that any connected bridgeless plane graph has a facial parity edge colouring with at most 92 coloursTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije