{"?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-RO9JQN7L/7AB097DB-F707-4C97-8549-D67DF589663D/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-RO9JQN7L/a9915f46-61fb-44fb-a76d-f9854759cd5c/PDF","dcterms:extent":"364 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-RO9JQN7L/10e54eb2-6e0f-4ec0-9c7c-7db3b162f851/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-RO9JQN7L","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2009","dc:creator":"Salamon, Gábor","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:2"},{"@xml:lang":"sl","#text":"str. 77-92"}],"dc:identifier":["COBISSID:15159897","ISSN:1855-3966","URN:URN:NBN:SI:doc-RO9JQN7L"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"sl","#text":"matematika"},{"@xml:lang":"sl","#text":"teorija grafov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Vulnerability bounds on the number of spanning tree leaves|"},"dc:description":{"@xml:lang":"sl","#text":"Hamiltonicity and vulnerability of graphs are in a strong connection. A basic necessary condition states that a graph containing a 2-leaf spanning tree (that is a Hamiltonian path) cannot be split into more than ?$k + 1$? components by deleting ?$k$? of its vertices. In this paper we consider a more general approach and investigate the connection between the number of spanning tree leaves and two vulnerability parameters namely scattering number sc?$(G)$? and cut-asymmetry ca?$(G)$?. We prove that any spanning tree of a graph ?$G$? has at least sc?$(G) + 1$? leaves. We also show that if ?$X \\subset V$? is a maximum cardinality independent set of ?$G = (V, E)$? such that the elements of ?$X$? are all leaves of a particular spanning tree then ?$|X| = {\\rm ca}(G) + 1 = |V| - {\\rm cvc}(G)$?, where cvc?$(G)$? is the size of a minimum connected vertex cover of ?$G$?. As a consequence we obtain a new proof for the following results: any spanning tree with independent leaves provides a 2-approximation for both Maximum Internal Spanning Tree and Minimum Connected Vertex Cover problems. We also consider the opposite point of view by fixing the number of leaves to ?$q$? and looking for a ?$q$?-leaf subtree of ?$G$? that spans a maximum number of vertices. Bermond proved that a 2-connected graph on ?$n$? vertices always contains a path (a 2-leaf subtree) of length min ?$\\{n,\\delta_2\\}$?, where ?$\\delta_2$? is the minimum degree-sum ofa 2-element independent set. We generalize this result to obtain a sufficient condition for the existence of a large ?$q$?-leaf subtree"},"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-RO9JQN7L","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-RO9JQN7L"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-RO9JQN7L/7AB097DB-F707-4C97-8549-D67DF589663D/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-RO9JQN7L/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-RO9JQN7L"}}}}