{"?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-U6VQ2HHQ/874cef2d-89e6-4be4-9857-d7d8bf23b3e2/PDF","dcterms:extent":"330 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-U6VQ2HHQ/c731de3f-63c8-4171-8e46-6d8b55a249fe/TEXT","dcterms:extent":"20 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-U6VQ2HHQ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":["Hibi, Takayuki","Mori, Aki","Ohsugi, Hidefumi","Shikama, Akihiro"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 323-332"}],"dc:identifier":["COBISSID:17833561","ISSN:1855-3966","URN:URN:NBN:SI:doc-U6VQ2HHQ"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"edge polytope"},{"@xml:lang":"en","#text":"finite simple graph"},{"@xml:lang":"sl","#text":"končni enostavni graf"},{"@xml:lang":"sl","#text":"povezavni politop"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The number of edges of the edge polytope of a finite simple graph|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$d \\ge 3$? be an integer. It is known that the number of edges of the edge polytope of the complete graph with ?$d$? vertices is ?$d(d-1)(d-2)/2$?. In this paper, we study the maximum possible number ?$\\mu_{d}$? of edges of the edge polytope arising from finite simple graphs with ?$d$? vertices. We show that ?$\\mu_{d} = d(d-1)(d-2)/2$? if and only if ?$3 \\leq d \\leq 14$?. In addition, we study the asymptotic behavior of ?$\\mu_{d}$?. Tran-Ziegler gave a lower bound for ?$\\mu_{d}$? by constructing a random graph. We succeeded in improving this bound by constructing both a non-random graph and a random graph whose complement is bipartite"},{"@xml:lang":"sl","#text":"Naj bo ?$d \\ge 3$? celo število. Znano je, da je število povezav povezavnega politopa polnega grafa z ?$d$? vozlišči enako ?$d(d-1)(d-2)/2$?. V tem članku študiramo največje možno število ?$\\mu_{d}$? povezav, ki jih lahko imajo povezavni politopi, dobljeni iz končnih enostavnih grafov z ?$d$? vozlišči. Pokažemo, da je ?$\\mu_{d} = d(d-1)(d-2)/2$? če in samo če ?$3 \\leq d \\leq 14$?. Poleg tega študiramo asimptotično vedenje števila ?$\\mu_{d}$?. Tran-Ziegler sta dobila spodnjo mejo za ?$\\mu_{d}$? tako, da sta konstruirala slučajni graf. Uspelo nam je izboljšati to mejo s konstruiranjem ne-slučajnega grafa in slučajnega grafa, katerega komplement je dvodelen"}],"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-U6VQ2HHQ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-U6VQ2HHQ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-U6VQ2HHQ/874cef2d-89e6-4be4-9857-d7d8bf23b3e2/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-U6VQ2HHQ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-U6VQ2HHQ"}}}}