{"?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-V2Z5F9ZG/eab909ad-341f-45c7-bb1b-9926f39bbfd3/PDF","dcterms:extent":"281 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-V2Z5F9ZG/de1987f8-da79-401c-b0cc-e9bca77c692e/TEXT","dcterms:extent":"22 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-V2Z5F9ZG","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Dupuis, Michael","Wagon, Stan"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 115-124"}],"dc:identifier":["COBISSID:17584985","ISSN:1855-3966","URN:URN:NBN:SI:doc-V2Z5F9ZG"],"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":"generalized Petersen graphs"},{"@xml:lang":"sl","#text":"graf skakačevih skokov"},{"@xml:lang":"en","#text":"Hamilton-connected"},{"@xml:lang":"en","#text":"Hamiltonian paths"},{"@xml:lang":"en","#text":"Hamilton-laceable"},{"@xml:lang":"sl","#text":"Hamiltonove poti"},{"@xml:lang":"sl","#text":"hamiltonsko-povezan"},{"@xml:lang":"sl","#text":"hamiltonsko-premostljiv"},{"@xml:lang":"en","#text":"knight graph"},{"@xml:lang":"sl","#text":"posplošeni Petersenovi grafi"},{"@xml:lang":"sl","#text":"sledljiv"},{"@xml:lang":"en","#text":"traceable"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Laceable knights|"},"dc:description":[{"@xml:lang":"sl","#text":"A bipartite graph is Hamilton-laceable if for any two vertices in different parts there is a Hamiltonian path from one to the other. Using two main ideas (an algorithm for finding Hamiltonian paths and a decomposition lemma to move from smaller cases to larger) we show that the graph of knight's moves on an ?$m \\times n$? board is Hamilton-laceable iff ?$m \\ge 6$?, ?$n \\ge 6$?, and one of ?$m$?, ?$n$? is even. We show how the algorithm leads to new conjectures about Hamiltonian paths for various families, such as generalized Petersen graphs, ?$I$?-graphs, and cubic symmetric graphs"},{"@xml:lang":"sl","#text":"Dvodelen graf je hamiltonsko-premostljiv če za poljubni dve vozlišči iz različnih delov obstaja Hamiltonova pot od enega do drugega. Z uporabo dveh glavnih idej (algoritem za najdenje Hamiltonovih poti in dekompozicijska lema za premik od manjših primerov k večjim) pokažemo, da je graf skakačevih skokov na ?$m \\times n$? šahovski deski Hamiltonsko-premostljiv če in samo če je ?$m \\ge 6$?, ?$n \\ge 6$?, in je eden od ?$m$?, ?$n$? sod. Pokažemo, kako algoritem vodi k novim domnevam o Hamiltonovih poteh za različne družine, kot so npr. generalizirani Petersenovi grafi, ?$I$?-grafi in kubični simetrični grafi"}],"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-V2Z5F9ZG","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-V2Z5F9ZG"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-V2Z5F9ZG/eab909ad-341f-45c7-bb1b-9926f39bbfd3/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-V2Z5F9ZG/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-V2Z5F9ZG"}}}}