{"?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-D3NYGZDH/c9322982-1ec8-4130-98cf-a9bda597ebbb/PDF","dcterms:extent":"1131 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-D3NYGZDH/a43dbd95-917b-4b32-a490-e0da9c068f57/TEXT","dcterms:extent":"39 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-D3NYGZDH/e354b179-04c6-451f-b78d-e7ce0e3825ae/PDF","dcterms:extent":"149 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-D3NYGZDH/01ab4ac0-9b19-44e9-aadb-2788a04a7491/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-D3NYGZDH","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":["Chen, Yaojun","Gao, Wei","Wang, Weifan"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1, article  p1.04"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-23"}],"dc:identifier":["DOI:10.26493/1855-3974.3161.63b","ISSN:1855-3974","COBISSID_HOST:288347907","URN:URN:NBN:SI:doc-D3NYGZDH"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:subject":[{"@xml:lang":"sl","#text":"delni k-faktor"},{"@xml:lang":"en","#text":"fractional k-factor"},{"@xml:lang":"sl","#text":"graf"},{"@xml:lang":"en","#text":"graph"},{"@xml:lang":"en","#text":"toughness"},{"@xml:lang":"en","#text":"toughness variant"},{"@xml:lang":"sl","#text":"trdnost"},{"@xml:lang":"sl","#text":"varianta trdnosti"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Tight toughness variant condition for fractional k-factors|"},"dc:description":[{"@xml:lang":"sl","#text":"The toughness t(G) of graph G is formalized as the minimum ratio of |S| and ?(G - S) over all vertex subsets S subject to ?(G - S) > 1. As the unique variant parameter of toughness, ?(G) is formulated as the minimum ratio of |S| and ?(G - S) - 1 traversing all the vertex subset S restricted to ?(G - S) ? 2. The extant contributions reveal that there is a substantial correlation between toughness and fractional factors. However, there is still a paucity of solid studies on toughness variants ?(G). This work provides several theoretical underpinnings for the tight toughness variant bound for a graph G which admits a fractional k-factor. To be specific, a graph G has a fractional k-factor if ?(G) > k for k ? 3 and if ?(G)>3/2 for k = 2. The sharpness of the given bounds is explained by counterexamples"},{"@xml:lang":"sl","#text":"Trdnost grafa t(G) grafa G je formalizirana kot najmanjše razmerje med |S| in ?(G - S) za vse podmnožice vozlišč S, kjer velja ?(G - S) > 1. Kot edini variantni parameter trdnosti je ? (G) definiran kot najmanjše razmerje med |S| in ?(G - S) - 1, pri čemer se pregledujejo vse podmnožice vozlišč S, za katere velja ?(G - S) ? 2. Obstoječi prispevki razkrivajo, da obstaja pomembna povezava med trdnostjo in delnimi faktorji. Vendar pa še vedno primanjkuje temeljitih raziskav o različicah trdnosti ? (G). To delo ponuja več teoretičnih temeljev za strogo mejo variante trdnosti za graf G, ki dopušča delni k-faktor. Natančneje, graf G ima delni k-faktor, če velja ? (G) > k za k ? 3 in če velja ? (G) > 3 2 za k = 2. Natančnost podanih mej je pojasnjena s protiprimeri"}],"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-D3NYGZDH","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-D3NYGZDH"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-D3NYGZDH/c9322982-1ec8-4130-98cf-a9bda597ebbb/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-D3NYGZDH/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-D3NYGZDH"}}}}