{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-9F0SHHWE/5cc6488f-e3de-476c-b0a8-2877b490fc9d/PDF","dcterms:extent":"285 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-9F0SHHWE/bb782971-8c2a-4cae-ac43-add6dede553f/TEXT","dcterms:extent":"25 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-9F0SHHWE","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Lužar, Borut","Petruševski, Mirko","Škrekovski, Riste"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 267-277"}],"dc:identifier":["ISSN:1855-3966","COBISSID:2048342547","URN:URN:NBN:SI:doc-9F0SHHWE"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"barvanje povezav"},{"@xml:lang":"en","#text":"edge coloring"},{"@xml:lang":"en","#text":"edge decompositon"},{"@xml:lang":"sl","#text":"grafi"},{"@xml:lang":"sl","#text":"lihi podgraf"},{"@xml:lang":"en","#text":"odd subgraph"},{"@xml:lang":"sl","#text":"povezavna dekompozicija"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Odd edge coloring of graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"An edge coloring of a graph ?$G$? is said to be an odd edge coloring if for each vertex ?$v$? of ?$G$? and each color ?$c$?, the vertex ?$v$? uses the color ?$c$? an odd number of times or does not use it at all. In L. Pyber, Covering the edges of a graph by..., Graphs and Numbers, Colloq. Math. Soc. János Bolyai 60 (1991), 583-610., Pyber proved that 4 colors suffice for an odd edge coloring of any simple graph. Recently, some results on this type of colorings of (multi)graphs were successfully applied in solving a problem of facial parity edge coloring B. Lužar and R. Škrekovski, Improved bound on facial parity edge coloring, Discrete Math. 313 (2013), 2218-2222 and J. Czap, S. Jendrol', F. Kardoš and R. Soták, Facial parity edge colouring of plane pseudographs, Disc. Math. 312 (2012), 2735-2740. In this paper we present additional results, namely we prove that 6 colors suffice for an odd edge coloring of any loopless connected (multi)graph, provide examples showing that this upper bound is sharp and characterize the family of loopless connected (multi)graphs for which the bound 6 is achieved. We also pose several open problems"},{"@xml:lang":"sl","#text":"Barvanje povezav grafa ?$G$? je liho barvanje povezav, če za vsako vozlišče ?$v$? grafa ?$G$? in za vsako barvo ?$c$?, vozlišče ?$v$? uporabi barvo ?$c$? lihokrat ali pa je sploh ne uporabi. V L. Pyber, Covering the edges of a graph by..., Graphs and Numbers, Colloq. Math. Soc. János Bolyai 60 (1991), 583-610. je Pyber dokazal, da 4 barve zadoščajo za liho povezavno barvanje vsakega enostavnega grafa. Nedavno so bili nekateri rezultati o tem tipu barvanj (multi)grafov uspešno uporabljeni pri reševanju problema parnosti lic povezavnega barvanja B. Lužar and R. Škrekovski, Improved bound on facial parity edge coloring, Discrete Math. 313 (2013), 2218-2222 in J. Czap, S. Jendrol', F. Kardoš and R. Soták, Facial parity edge colouring of plane pseudographs, Disc. Math. 312 (2012), 2735-2740. V tem članku predstavimo dodatne rezultate, in sicer dokažemo, da 6 barv zadošča za liho povezavno barvanje vsakega povezanega (multi)grafa brez zank, navedemo primere, ko je ta zgornja meja dosežena, in karakteriziramo družino povezanih (multi)grafov brez zank, pri katerih je meja 6 dosežena. Predstavimo tudi nekaj odprtih problemov"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-9F0SHHWE","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-9F0SHHWE"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-9F0SHHWE/5cc6488f-e3de-476c-b0a8-2877b490fc9d/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-9F0SHHWE/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-9F0SHHWE"}}}}