{"?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-VOMDSDSP/135b1b61-3e61-4d30-944f-3894aa437600/PDF","dcterms:extent":"1059 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-VOMDSDSP/425ea534-3ac5-4724-a453-680b6e74e9ad/TEXT","dcterms:extent":"44 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-VOMDSDSP","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["Álvarez López, Jesús Antonio","Barral Lijó, Ramón","Nozawa, Hiraku"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:21"},{"@xml:lang":"sl","#text":"str. 71-88"}],"dc:identifier":["DOI:10.26493/1855-3974.2354.616","COBISSID_HOST:111484931","ISSN:1855-3966","URN:URN:NBN:SI:doc-VOMDSDSP"],"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":"barvanje"},{"@xml:lang":"en","#text":"coarse"},{"@xml:lang":"en","#text":"distinguishing"},{"@xml:lang":"sl","#text":"graf"},{"@xml:lang":"en","#text":"graph coloring"},{"@xml:lang":"sl","#text":"grob"},{"@xml:lang":"en","#text":"growth"},{"@xml:lang":"sl","#text":"rast"},{"@xml:lang":"sl","#text":"razlikovanje"},{"@xml:lang":"sl","#text":"simetrija"},{"@xml:lang":"en","#text":"symmetry"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Coarse distinguishability of graphs with symmetric growth|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$X$? be a connected, locally finite graph with symmetric growth. We prove that there is a vertex coloring ?$\\phi : X \\rightarrow \\{0, 1\\}$? and some ?$R \\in \\mathbb{R}$? such that every automorphism ?$f$? preserving ?$\\phi$? is ?$R$?-close to the identity map; this can be seen as a coarse geometric version of symmetry breaking. We also prove that the infinite motion conjecture is true for graphs where at least one vertex stabilizer ?$S_x$? satisfies the following condition: for every non-identity automorphism ?$f \\in S_x$?, there is a sequence ?$x_n$? such that ?$\\lim d(x_n, f(x_n)) = \\infty $?"},{"@xml:lang":"sl","#text":"Naj bo ?$X$? povezan, lokalno končen graf s simetrično rastjo. Dokažemo, da obstaja barvanje točk ?$\\phi : X \\rightarrow \\{0, 1\\}$? in neko število ?$R \\in \\mathbb{R}$?, za katerega velja, da se vsak avtomorfizem ?$f$?, ki ohranja ?$\\phi$?, v vsaki točki razlikuje od identitete največ za ?$R$?; to lahko imamo za grobo geometrijsko različico zloma simetrije. Dokažemo tudi, da je domneva o neskončnem gibanju resnična za grafe, pri katerih najmanj en točkovni stabilizator ?$S_x$? zadošča naslednjemu pogoju: za vsak neidentični avtomorfizem ?$f \\in S_x$? obstaja zaporedje ?$x_n$?, za katerega velja ?$\\lim d(x_n, f(x_n)) = \\infty $?"}],"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-VOMDSDSP","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-VOMDSDSP"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-VOMDSDSP/135b1b61-3e61-4d30-944f-3894aa437600/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-VOMDSDSP/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-VOMDSDSP"}}}}