{"?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-ORYIXTKO/febf5e7d-dfac-4e19-9e26-48ed950a79af/PDF","dcterms:extent":"1428 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-ORYIXTKO/03a93783-e39f-4bda-9afd-66faf63a5f72/TEXT","dcterms:extent":"57 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-ORYIXTKO","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["García Olaverri, Alfredo","Pilz, Alexander","Tejel Altarriba, Javier"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:20"},{"@xml:lang":"sl","#text":"str. 69-87"}],"dc:identifier":["DOI:10.26493/1855-3974.2226.e93","ISSN:1855-3966","COBISSID_HOST:91107075","URN:URN:NBN:SI:doc-ORYIXTKO"],"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":"graf"},{"@xml:lang":"en","#text":"graph"},{"@xml:lang":"en","#text":"NP-complete problem"},{"@xml:lang":"sl","#text":"NP-poln problem"},{"@xml:lang":"en","#text":"plane subgraph"},{"@xml:lang":"sl","#text":"ravninsko vložen podgraf"},{"@xml:lang":"en","#text":"topological drawing"},{"@xml:lang":"sl","#text":"topološka risba"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On plane subgraphs of complete topological drawings|"},"dc:description":[{"@xml:lang":"sl","#text":"Topological drawings are representations of graphs in the plane, where vertices are represented by points, and edges by simple curves connecting the points. A drawing is simple if two edges intersect at most in a single point, either at a common endpoint or at a proper crossing. In this paper we study properties of maximal plane subgraphs of simple drawings ?$D_n$? of the complete graph ?$K_n$? on ?$n$? vertices. Our main structural result is that maximal plane subgraphs are 2-connected and what we call essentially 3-edge-connected. Besides, any maximal plane subgraph contains at least ?$\\lceil 3 n/2 \\rceil$? edges. We also address the problem of obtaining a plane subgraph of ?$D_n$? with the maximum number of edges, proving that this problem is NP-complete. However, given a plane spanning connected subgraph of ?$D_n$?, a maximum plane augmentation of this subgraph can be found in ?$O(n^3)$? time. As a side result, we also show that the problem of finding a largest compatible plane straight-line graph of two labeled point sets is NP-complete"},{"@xml:lang":"sl","#text":"Topološke risbe so predstavitve grafov v ravnini, pri katerih so vozlišča grafa predstavljene s točkami v ravnini, povezave pa z enostavnimi krivuljami, ki povezujejo točke. Risba je enostavna, če se dve povezavi sekata kvečjemu v eni točki in to bodisi v skupnem krajiš ču bodisi v pravem presečišču. V tem članku raziskujemo lastnosti maksimalnih ravninsko vloženih podgrafov enostavnih risb ?$D_n$? polnega grafa ?$K_n$? na ?$n$? vozliščih. Naš glavni strukturni rezultat je, da so maksimalni ravninsko vloženi podgrafi 2-povezani, pa tudi, da so, kot smo to poimenovali, bistveno 3-povezavno-povezani. Pokažemo tudi, da vsak maksimalni ravninsko vložen podgraf vsebuje najmanj ?$\\lceil 3 n/2 \\rceil$? povezav. Obravnavamo tudi problem iskanja ravninsko vloženega podgrafa risbe ?$D_n$? z maksimalnim številom povezav in dokažemo, da je ta problem NP-poln. Kljub temu pa je, če je podan ravninsko vložen vpeti povezani podgraf risbe ?$D_n$?, mogoče najti maksimalno ravninsko razširitev tega podgrafa v času ?$O(n^3)$?. Ob tem pokažemo tudi, da je problem iskanja največjega kompatibilnega ravninsko vloženega grafa z ravnimi črtami, ki ima dve označeni množici vozlišč, NP-poln"}],"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-ORYIXTKO","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-ORYIXTKO"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-ORYIXTKO/febf5e7d-dfac-4e19-9e26-48ed950a79af/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-ORYIXTKO/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-ORYIXTKO"}}}}