{"?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-0N1UURJ6/d7a942d9-1671-47f6-b2f5-4a270adde13f/PDF","dcterms:extent":"395 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-0N1UURJ6/0c8d9b4b-1006-40e8-af4b-978b55b201fe/TEXT","dcterms:extent":"40 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-0N1UURJ6","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Brinkmann, Gunnar","Ozeki, Kenta","Van Cleemput, Nico"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"str. 51-66"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18912089","URN:URN:NBN:SI:doc-0N1UURJ6"],"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":"3-sprehod"},{"@xml:lang":"en","#text":"3-walk"},{"@xml:lang":"sl","#text":"dominacija"},{"@xml:lang":"en","#text":"domination"},{"@xml:lang":"sl","#text":"graf"},{"@xml:lang":"en","#text":"graph"},{"@xml:lang":"en","#text":"Hamiltonian cycle"},{"@xml:lang":"sl","#text":"hamiltonski cikel"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Types of triangle in Hamiltonian triangulations and an application to domination and k-walks|"},"dc:description":[{"@xml:lang":"sl","#text":"We investigate the minimum number ?$t_0(G)$? of faces in a Hamiltonian triangulation ?$G$? so that any Hamiltonian cycle ?$C$? of ?$G$? has at least ?$t_0(G)$? faces that do not contain an edge of ?$C$?. We prove upper and lower bounds on the maximum of these numbers for all triangulations with a fixed number of facial triangles. Such triangles play an important role when Hamiltonian cycles in triangulations with 3-cuts are constructed from smaller Hamiltonian cycles of 4-connected subgraphs. We also present results linking the number of these triangles to the length of 3-walks in a class of triangulation and to the domination number"},{"@xml:lang":"sl","#text":"Raziskujemo število ?$t_0(G)$?, tj. minimalno število lic v neki hamiltonski triangulaciji ?$G$?, tako da ima vsak hamiltonski cikel ?$C$? v ?$G$? vsaj ?$t_0(G)$? lic, ki ne vsebujejo povezave iz ?$C$?. Dokažemo zgornje in spodnje meje za maksimum teh števil za vse triangulacije s fiksnim številom trikotniških lic. Takšni trikotniki igrajo pomembno vlogo, ko v triangulacijah s 3-prerezi konstruiramo hamiltonski cikel iz manjših hamiltonskih ciklov 4-povezanih podgrafov. Predstavimo tudi rezultate, ki povezujejo število teh trikotnikov z dolžino 3-sprehodov v razredu triangulacij in z dominacijskim številom"}],"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-0N1UURJ6","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-0N1UURJ6"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-0N1UURJ6/d7a942d9-1671-47f6-b2f5-4a270adde13f/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-0N1UURJ6/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-0N1UURJ6"}}}}