{"?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-V9D75SDV/3afe8bd7-ae65-4d63-a0fe-5bf673334dc8/PDF","dcterms:extent":"1673 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-V9D75SDV/db10e1cb-3de8-43a8-8f70-d6f495aa4702/TEXT","dcterms:extent":"34 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-V9D75SDV","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["Jin, Xian'an","Yan, Qi"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"P2.06 (16 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2053.c7b","COBISSID_HOST:116452099","ISSN:1855-3966","URN:URN:NBN:SI:doc-V9D75SDV"],"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":"A-tir"},{"@xml:lang":"en","#text":"A-trails"},{"@xml:lang":"en","#text":"checkerboard colourable"},{"@xml:lang":"en","#text":"embedded graphs"},{"@xml:lang":"en","#text":"Eulerian"},{"@xml:lang":"sl","#text":"Eulerjev obhod"},{"@xml:lang":"sl","#text":"šahovnično pobarvljiv"},{"@xml:lang":"en","#text":"twisted duals"},{"@xml:lang":"sl","#text":"vloženi grafi"},{"@xml:lang":"sl","#text":"zasukani duali"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A-trails of embedded graphs and twisted duals|"},"dc:description":[{"@xml:lang":"sl","#text":"Kotzig showed that every connected 4-regular plane graph has an ?$A$?-trail -- an Eulerian circuit that turns either left or right at each vertex. However, this statement is not true for Eulerian plane graphs and determining if an Eulerian plane graph has an ?$A$?-trail is NP-hard. The aim of this paper is to give a characterization of Eulerian embedded graphs having an ?$A$?-trail. Andersen et al. showed the existence of orthogonal pairs of ?$A$?-trails in checkerboard colourable 4-regular graphs embedded on the plane, torus and projective plane. A problem posed in their paper is to characterize Eulerian embedded graphs (not necessarily checkerboard colourable) which contain two orthogonal ?$A$?-trails. In this article, we solve this problem in terms of twisted duals. Several related results are also obtained"},{"@xml:lang":"sl","#text":"Kotzig je dokazal, da ima vsak povezan 4-regularen ravninski graf ?$A$?-tir: Eulerjev obhod, ki v vsakem vozlišču zavije bodisi levo bodisi desno. Ta ugotovitev pa ne drži za Eulerjeve ravninske grafe, in ugotavljanje, ali ima neki Eulerjev ravninski graf ?$A$?-tir, je NP-težak problem. Cilj tega članka je karakterizirati tiste Eulerjeve vložene grafe, ki imajo ?$A$?-tir. Andersen in dr. so dokazali obstoj ortogonalnih parov ?$A$?-tirov v šahovnično pobarvljivih 4-regularnih grafih, vloženih v ravnino, torus in projektivno ravnino. V svojem članku so zastavili problem karakterizacije Eulerjevih vloženih grafov (ne nujno šahovnično pobarvljivih), ki vsebujejo dva pravokotna ?$A$?-tira. V tem članku ta problem rešimo s pomočjo zasukanih dualov. Na ta način dobimo še nekaj sorodnih rezultatov"}],"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-V9D75SDV","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-V9D75SDV"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-V9D75SDV/3afe8bd7-ae65-4d63-a0fe-5bf673334dc8/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-V9D75SDV/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-V9D75SDV"}}}}