{"?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-7Z26HAOE/7821bcc4-8139-484d-8f26-981fec5ed38f/PDF","dcterms:extent":"356 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7Z26HAOE/7de8ceb9-dc1a-4241-84cc-6175f6de4f4f/TEXT","dcterms:extent":"24 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-7Z26HAOE","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":["Allagan, Julian D.","Voloshin, Vitaly"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"str. 173-182"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18704729","URN:URN:NBN:SI:doc-7Z26HAOE"],"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":"2-drevo"},{"@xml:lang":"en","#text":"2-tree"},{"@xml:lang":"sl","#text":"maksimalen zunanjeravninski"},{"@xml:lang":"en","#text":"maximal outerplanar"},{"@xml:lang":"en","#text":"partition"},{"@xml:lang":"sl","#text":"razdelitev"},{"@xml:lang":"en","#text":"Stirling numbers"},{"@xml:lang":"sl","#text":"Stirlingova števila"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"F-WORM colorings of some 2-trees: partition vectors|"},"dc:description":[{"@xml:lang":"sl","#text":"Suppose ?$\\mathscr{F} = \\{F_1, \\ldots, F_t\\}$? is a collection of distinct subgraphs of a graph ?$G = (V, E)$?. An ?$\\mathscr{F}$?-WORM coloring of ?$G$? is the coloring of its vertices such that no copy of each subgraph ?$F_i \\in \\mathscr{F}$? is monochrome or rainbow. This generalizes the notion of ?$F$?-WORM coloring that was introduced recently by W. Goddard et al. Congr. Numerantium 219, 161--173 (2014). A (restricted) partition vector ?$(\\zeta_{\\alpha}, \\ldots, \\zeta_{\\beta})$? is a sequence whose terms ?$\\zeta_r$? are the number of ?$\\mathscr{F}$?-WORM colorings using exactly ?$r$? colors, with ?$\\alpha \\leq r \\leq \\beta$?. The partition vectors of complete graphs and those of some 2-trees are discussed. We show that, although 2-trees admit the same partition vector in classic proper vertex colorings which forbid monochrome ?$K_2$?, their partition vectors in ?$K_3$?-WORM colorings are different"},{"@xml:lang":"sl","#text":"Naj bo ?$\\mathscr{F} = \\{F_1, \\ldots, F_t\\}$? zbirka različnih podgrafov grafa ?$G = (V, E)$?. ?$\\mathscr{F}$?-WORM barvanje grafa ?$G$? je takšno barvanje njegovih vozlišč, pri katerem nobena kopija nobenega od podgrafov ?$F_i \\in \\mathscr{F}$? ni ne enobarvna ne mavrična. To je posplošitev pojma ?$F$?-WORM barvanja, ki so ga nedavno vpeljali W. Goddard, K. Wash in H. Xu. (Omejen) razdelitveni vektor ?$(\\zeta_{\\alpha}, \\ldots, \\zeta_{\\beta})$? je zaporedje, katerega členi ?$\\zeta_r$? so števila ?$\\mathscr{F}$?-WORM barvanj z natanko ?$r$? barvami, kjer je ?$\\alpha \\leq r \\leq \\beta$?. Obravnavamo razdelitvene vektorje polnih grafov in nekaterih 2-dreves. Pokažemo, da četudi 2-drevesa premorejo enake razdelitvene vektorje pri klasičnem pravilnem barvanju vozlišč, ki prepoveduje enobarvne ?$K_2$?, so njihovi razdelitveni vektorji v ?$K_3$?-WORM barvanju lahko različni"}],"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-7Z26HAOE","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-7Z26HAOE"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-7Z26HAOE/7821bcc4-8139-484d-8f26-981fec5ed38f/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-7Z26HAOE/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-7Z26HAOE"}}}}