{"?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-18MFNMNA/7012e596-d371-4ec1-8ec4-5a3e7713f2d8/PDF","dcterms:extent":"339 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-18MFNMNA/a7dac9e5-ec11-485a-9d30-d5a296ba275a/TEXT","dcterms:extent":"44 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-18MFNMNA/54669655-dd93-48e4-9fd7-2e3c8d65fdd4/PDF","dcterms:extent":"150 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-18MFNMNA/bb2eb59e-1953-43f4-8ce5-3c62ba448a33/TEXT","dcterms:extent":"3 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-18MFNMNA","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2026","dc:creator":["Bickle, Allan","Brinkmann, Gunnar"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1, article  p1.03"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-15"}],"dc:identifier":["DOI:10.26493/1855-3974.3066.5bf","ISSN:1855-3974","COBISSID_HOST:288315907","URN:URN:NBN:SI:doc-18MFNMNA"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:subject":[{"@xml:lang":"sl","#text":"2-drevo"},{"@xml:lang":"en","#text":"2-tree"},{"@xml:lang":"en","#text":"Hamiltonian cycle"},{"@xml:lang":"sl","#text":"hamiltonski cikel"},{"@xml:lang":"sl","#text":"triangulacija"},{"@xml:lang":"en","#text":"triangulation"},{"@xml:lang":"en","#text":"Yutsis partition"},{"@xml:lang":"sl","#text":"Yutsisova particija"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Plane triangulations without large 2-trees|"},"dc:description":[{"@xml:lang":"sl","#text":"In 1995 Leizhen Cai asked whether each plane triangulation has a spanning 2-tree. This question was recently answered in the negative by Bickle. He gave a plane triangulation on 38 vertices for which each 2-tree contained in it misses at least one vertex. We give a smaller example on 29 vertices and show that for each c>0 there are plane triangulations P=(V,E), so that each 2-tree that is a subgraph of P contains fewer than c|V| vertices. We also give a lower bound for the size of a maximum 2-tree in plane triangulations by proving that each plane triangulation P=(V,E) contains a 2-tree on at least log_2 (|V|-1)+4 -log_2 3 vertices. Finally we give structural criteria based on the decomposition trees of Jackson and Yu that guarantee the existence of spanning 2-trees in plane triangulations. The results are proven by using the close relation of 2-trees to hamiltonian cycles and to induced trees in the dual for plane triangulations without separating triangles"},{"@xml:lang":"sl","#text":"Leta 1995 je Leizhen Cai vprašal, ali ima vsaka ravninska triangulacija razpenjajoče se 2-drevo. Na to vprašanje je nedavno negativno odgovoril Bickle. Podal je ravninsko triangulacijo s 38 vozlišči, za katero vsako 2-drevo, ki je vsebovano v njej, izpusti vsaj eno vozlišče. Mi podamo manjši primer s 29 vozlišči in pokažemo, da za vsako c > 0 obstajajo ravninske triangulacije P = (V, E), tako da vsako 2-drevo, ki je podgraf P , vsebuje manj kot c|V | vozlišč. Podamo tudi spodnjo mejo za velikost največjega 2-drevesa v ravninskih triangulacijah, tako da dokažemo, da vsaka ravninska triangulacija P = (V, E) vsebuje 2-drevo z vsaj log2(|V | - 1) + 4 - log2 3 vozlišči. Nazadnje podamo strukturna merila, ki temeljijo na dekompozicijskih drevesih Jacksona in Yuja, in zagotavljajo obstoj razpenjajočih se 2-dreves v ravninskih triangulacijah. Rezultati so dokazani z uporabo tesne povezave med 2-drevesi, hamiltonskimi cikli in induciranimi drevesi v dualu za ravninske triangulacije brez ločevalnih trikotnikov"}],"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-18MFNMNA","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-18MFNMNA"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-18MFNMNA/7012e596-d371-4ec1-8ec4-5a3e7713f2d8/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-18MFNMNA/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-18MFNMNA"}}}}