0 KB249 KB40 KB200820252008Mohar, BojanSteffen, EckhardVodopivec, Andrejletnik:1številka:2str. 169-184COBISSID:15147865ISSN:1855-3966URN:URN:NBN:SI:doc-VBD6X484enDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneamatematikateorija grafovRelating embedding and coloring properties of snarks|In 1969, Grünbaum conjectured that snarks do not have polyhedral embeddings into orientable surfaces. We define the defect of a graph and use it to study embeddings of superpositions of cubic graphs into orientable surfaces. Superposition was introduced by Kochol to construct snarks with arbitrary large girth. It is shown that snarks constructed by Kochol do not have polyhedral embeddings into orientable surfaces. For each ?$k \ge 2$? we construct infinitely many snarks with defect precisely ?$k$?. We then relate the defect with the resistance ?$r(G)$? of a cubic graph ?$G$? which is the size of a minimum color class of a 4-edge-coloring of ?$G$?. These results are then extended to deal with some weaker versions of the Grünbaum ConjectureTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije