{"?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-7KIOPH38/5cc845f0-0316-4756-86d5-0390875c8d5d/PDF","dcterms:extent":"370 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-7KIOPH38/f02bba9b-4104-4ed2-84f5-f624807c6e63/TEXT","dcterms:extent":"39 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-7KIOPH38","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":["Henning, Michael A.","Rall, Douglas F."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:20"},{"@xml:lang":"sl","#text":"str. 129-142"}],"dc:identifier":["DOI:10.26493/1855-3974.2227.e1a","ISSN:1855-3966","COBISSID_HOST:91621123","URN:URN:NBN:SI:doc-7KIOPH38"],"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":"competition-enclaveless gam"},{"@xml:lang":"sl","#text":"dominacijska igra"},{"@xml:lang":"en","#text":"domination game"},{"@xml:lang":"sl","#text":"tekmovalna brezenklavna igra"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The enclaveless competition game|"},"dc:description":[{"@xml:lang":"sl","#text":"For a subset ?$S$? of vertices in a graph ?$G$?, a vertex ?$v \\in S$? is an enclave of ?$S$? if ?$v$? and all of its neighbors are in ?$S$?, where a neighbor of ?$v$? is a vertex adjacent to ?$v$?. A set ?$S$? is enclaveless if it does not contain any enclaves. The enclaveless number ?$\\Psi(G)$? of ?$G$? is the maximum cardinality of an enclaveless set in ?$G$?. As first observed in P. J. Slate, J. Res. Natl. Bur. Stand. 82, 197-202 (1977), if $G$ is a graph with ?$n$? vertices, then ?$\\gamma(G) + \\Psi(G) = n$? where ?$\\gamma(G)$? is the well-studied domination number of ?$G$?. In this paper, we continue the study of the competition-enclaveless game introduced in 2001 by J. B. Philips and P. J. Slater \"An introduction to graph competition independence and enclaveless parameters\", Graph Theory Notes N. Y. 41, 37-41 (2001) and defined as follows. Two players take turns in constructing a maximal enclaveless set ?$S$?, where one player, Maximizer, tries to maximize ?$|S|$? and one player, Minimizer, tries to minimize ?$|S|$?. The competition-enclaveless game number ?$\\Psi_g^+(G)$? of ?$G$? is the number of vertices played when Maximizer starts the game and both players play optimally. We study among other problems the conjecture that if ?$G$? is an isolate-free graph of order ?$n$?, then ?$\\Psi_g^+(G) \\geq \\frac{1}{2} n$?. We prove this conjecture for regular graphs and for claw-free graphs"},{"@xml:lang":"sl","#text":"Če je ?$S$? podmnožica vozlišč grafa ?$G$?, potem vozlišču ?$v \\in S$? pravimo enklava množice ?$S$?, če je vozlišče ?$v$?, pa tudi vsi njegovi sosedje, v množici ?$S$?, pri čemer je sosed vozlišča v tisto vozlišče, ki je sosedno vozlišču ?$v$?. Množica ?$S$? je brezenklavna, če nima enklav. Brezenklavno število ?$\\Psi(G)$? grafa ?$G$? je kardinalnost največje brezenklavne množice v ?$G$?. Kot je prvi opazil Slater leta 1997: če je ?$G$? graf na ?$n$? vozliščih, potem je ?$\\gamma(G) + \\Psi(G) = n$?, kjer je ?$\\gamma(G)$? dobro raziskano dominacijsko število grafa ?$G$?. V članku nadaljujemo raziskavo tekmovalne brezenklavne igre, ki sta jo leta 2001 vpeljala Philips in Slater in je definirana takole: dva igralca izmenično konstruirata maksimalno brezenklavno množico ?$S$?, pri čemer en igralec, povečevalec, poizkuša maksimalizirati ?$|S|$?, drug igralec, pomanjševalec, pa poizkuša minimalizirati ?$|S|$?. Vrednost tekmovalne brezenklavne igre ?$\\Psi_g^+(G)$? grafa ?$G$? je število vozlišč, dobljenih v primeru, da povečevalec začne igro in da oba igralca igrata optimalno. Poleg drugih problemov raziskujemo domnevo, da če je ?$G$? graf brez izoliranih vozlišč reda ?$n$?, potem je ?$\\Psi_g^+(G) \\geq \\frac{1}{2} n$?. To domnevo dokažemo za regularne grafe in za brezkrempljaste grafe"}],"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-7KIOPH38","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-7KIOPH38"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-7KIOPH38/5cc845f0-0316-4756-86d5-0390875c8d5d/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-7KIOPH38/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-7KIOPH38"}}}}