{"?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-LMOY5732/1f77ebde-7982-44eb-b996-1571c6725c1a/PDF","dcterms:extent":"389 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-LMOY5732/2ee89035-cd7a-4bbb-aca6-dd3091a7c65e/TEXT","dcterms:extent":"45 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-LMOY5732","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["Drgas-Burchardt, Ewa","Drzystek, Agata","Sidorowicz, Elżbieta"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"P1.05 (15 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2083.e80","COBISSID_HOST:115433219","ISSN:1855-3966","URN:URN:NBN:SI:doc-LMOY5732"],"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":"?$\\theta $?-hipergrafi"},{"@xml:lang":"en","#text":"?$\\theta $?-hypergraphs"},{"@xml:lang":"sl","#text":"hipergrafi"},{"@xml:lang":"en","#text":"hypergraphs"},{"@xml:lang":"en","#text":"sum-llist-colouring"},{"@xml:lang":"sl","#text":"vsotno seznamsko barvanje"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Sum-list-colouring of theta-hypergraphs|"},"dc:description":[{"@xml:lang":"sl","#text":"Given a hypergraph ?$\\mathcal{H}$? and a function ?$f:V( \\mathcal{H}) \\rightarrow \\mathbb{N}$?, we say that ?$\\mathcal{H}$? is ?$f$?-choosable if there is a proper vertex coloring ?$\\phi$? of ?$\\mathcal{H}$? such that ?$\\phi(v) \\in L(v)$? for all ?$v\\in V(\\mathcal{H})$?, where ?$L:V( \\mathcal{H}) \\rightarrow 2^{\\mathbb{N}}$? is any assignment of ?$f(v)$? colors to a vertex ?$v$?. The sum choice number ?$\\chi_{sc}(\\mathcal{H})$? of ?$\\mathcal{H}$? is defined to be the minimum of ?$\\sum_{v \\in V(\\mathcal{H})} f(v)$? over all functions ?$f$? such that ?$\\mathcal{H}$? is ?$f$?-choosable. A trivial upper bound on ?$\\chi_{sc} (\\mathcal{H})$? is ?$|V( \\mathcal{H}|) + | \\mathcal{E}(\\mathcal{H})|$?. The class ?$\\Gamma_{sc}$? of hypergraphs that achieve this bound is induced hereditary. We analyze some properties of hypergraphs in ?$\\Gamma_{sc}$? as well as properties of hypergraphs in the class of forbidden hypergraphs for ?$\\Gamma_{sc}$?. We characterize all ?$\\theta $?-hypergraphs in ?$\\Gamma_{sc}$?, which leads to the characterization of all ?$\\theta$?-hypergraphs that are forbidden for ?$\\Gamma_{sc}$?"},{"@xml:lang":"sl","#text":"Če sta dana hipergraf ?$\\mathcal{H}$? in funkcija ?$f:V( \\mathcal{H}) \\rightarrow \\mathbb{N} $?, pravimo, da je ?$\\mathcal{H}$? ?$f$?-izbiren, če obstaja pravilno vozliščno barvanje ?$\\phi$?, pri katerem je ?$\\phi(v) \\in L(v)$? za vsa vozlišča ?$v\\in V(\\mathcal{H})$?, kjer je ?$L:V( \\mathcal{H}) \\rightarrow 2^{\\mathbb{N}}$? poljubna dodelitev ?$f(v)$? barv vozlišča ?$v$?. Vsotno izbirni indeks ?$\\chi_{sc}(\\mathcal{H})$? hipergrafa ?$\\mathcal{H}$? je definiran kot minimum vsote ?$\\sum_{v \\in V(\\mathcal{H})} f(v)$? po vseh funkcijah ?$f$?, za katere je ?$\\mathcal{H}$? ?$f$?-izbiren. Trivialna zgornja meja za ?$\\chi_{sc} (\\mathcal{H})$? je ?$|V(\\mathcal{H}|) + |\\mathcal{E} \\mathcal{H})|$?. Razred ?$\\Gamma_{sc}$? hipergrafov, ki dosežejo to mejo, je induciran hereditarno. Analiziramo nekaj lastnosti hipergrafov iz razreda ?$\\Gamma_{sc}$?, pa tudi lastnosti hipergrafov iz razreda prepovedanih hipergrafov za ?$\\Gamma_{sc}$?. Karakteriziramo vse ?$\\theta$?-hipergrafe iz razreda ?$\\Gamma_{sc}$?, od tod pa dobimo tudi karakterizacijo vseh ?$\\theta$?-hipergrafov, ki so prepovedani za ?$\\Gamma_{sc}$?"}],"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-LMOY5732","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-LMOY5732"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-LMOY5732/1f77ebde-7982-44eb-b996-1571c6725c1a/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-LMOY5732/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-LMOY5732"}}}}