{"?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-JVVHZ0TM/e3ce5400-00cf-43e4-b7cd-f87cc6f5d9d3/PDF","dcterms:extent":"271 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-JVVHZ0TM/193d5bd6-89ca-4c2b-abb6-bce2b5112816/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-JVVHZ0TM","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Levit, Vadim E.","Mandrescu, Eugen"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:18"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 359-369"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:42128899","URN:URN:NBN:SI:doc-JVVHZ0TM"],"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":"annihilation number"},{"@xml:lang":"en","#text":"annihilation set"},{"@xml:lang":"en","#text":"König-Egerváry graph"},{"@xml:lang":"sl","#text":"König-Egerváryjev graf"},{"@xml:lang":"sl","#text":"maksimalna neodvisna množica"},{"@xml:lang":"sl","#text":"maksimalno prirejanje"},{"@xml:lang":"en","#text":"maximum independent set"},{"@xml:lang":"en","#text":"maximum matching"},{"@xml:lang":"sl","#text":"množica s pragom"},{"@xml:lang":"sl","#text":"prag"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On an annihilation number conjecture|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$\\alpha(G)$? denote the cardinality of a maximum independent set, while ?$\\mu(G)$? be the size of a maximum matching in the graph ?$G=(V, E)$?. If ?$\\alpha(G)+\\mu(G)=|V|$?, then ?$G$? is a König-Egerváry graph. If ?$d_1 \\leq d_2 \\leq \\cdots \\leq d_n$? is the degree sequence of ?$G$?, then the annihilation number ?$a(G)$? of ?$G$? is the largest integer ?$k$? such that ?$\\sum_{i=1}^{k}d_i \\leq |E|$?. A set ?$A\\subseteq V$? satisfying ?$\\sum_{v\\in A} \\text{deg}(v)\\leq |E|$? is an annihilation set, if, in addition, ?$\\text{deg}(x) +\\sum_{v\\in A} \\text{deg}(v)>|E|$?, for every vertex ?$x\\in V(G)-A$?, then ?$A$? is a maximal annihilation set in ?$G$?. In 2011, Larson and Pepper conjectured that the following assertions are equivalent: (i) ?$\\alpha(G) =a(G)$?; (ii) ?$G$? is a König-Egerváry graph and every maximum independent set is a maximal annihilating set. It turns out that the implication \"(i) ?$\\Longrightarrow$? (ii)\" is correct. In this paper, we show that the opposite direction is not valid, by providing a series of generic counterexamples"},{"@xml:lang":"sl","#text":"Naj ?$\\alpha(G)$? označuje moč maksimalne neodvisne množice, ?$\\mu(G)$? pa velikost maksimalnega prirejanja v grafu ?$G=(V, E)$?. Če je ?$\\alpha(G)+\\mu(G)=|V|$?, potem je ?$G$? König-Egerváryjev graf. Če je ?$d_1 \\leq d_2 \\leq \\cdots \\leq d_n$? stopenjsko zaporedje grafa ?$G$?, potem je prag ?$a(G)$? grafa ?$G$? največje celo število ?$k$?, pri katerem je ?$\\sum_{i=1}^{k}d_i \\leq |E|$?. Množica ?$A\\subseteq V$?, ki zadošča pogoju? $\\sum_{v\\in A} \\text{deg}(v)\\leq |E|$?, se imenuje množica s pragom; če velja poleg tega ?$\\text{deg}(x) +\\sum_{v\\in A} \\text{deg}(v)>|E|$? za vsako točko ?$x\\in V(G)-A$?, potem je ?$A$? maksimalna množica s pragom v ?$G$?. Leta 2011 sta Larson in Pepper postavila domnevo o enakovrednosti naslednjih trditev: (i) ?$\\alpha(G) =a(G)$?; (ii) ?$G$? je König-Egerváryjev graf in vsaka maksimalna neodvisna množica je maksimalna množica s pragom. Izkazalo se je, da je implikacija\"(i) ?$\\Longrightarrow$? (ii)\" pravilna. V članku dokažemo, da obratna implikacija ne velja, prikažemo pa tudi vrsto generičnih protiprimerov"}],"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-JVVHZ0TM","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-JVVHZ0TM"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-JVVHZ0TM/e3ce5400-00cf-43e4-b7cd-f87cc6f5d9d3/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-JVVHZ0TM/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-JVVHZ0TM"}}}}