{"id":"https://openalex.org/W1573541561","doi":"https://doi.org/10.11575/cdm.v5i1.61894","title":"A characterization of the base-matroids of a graphic matroid","display_name":"A characterization of the base-matroids of a graphic matroid","publication_year":2007,"publication_date":"2007-01-21","ids":{"openalex":"https://openalex.org/W1573541561","doi":"https://doi.org/10.11575/cdm.v5i1.61894","mag":"1573541561"},"language":"en","primary_location":{"id":"pmh:oai:re.public.polimi.it:11311/570333","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/570333","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.11575/cdm.v5i1.61894","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053677027","display_name":"Francesco Maffioli","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maffioli, Francesco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042769467","display_name":"Norma Zagaglia Salvi","orcid":"https://orcid.org/0000-0003-1804-8566"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zagaglia Salvi, Norma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.06056462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":"1","first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9811000227928162,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.9872068166732788},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8824329376220703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8062717318534851},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7028824687004089},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.6417651176452637},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5891541242599487},{"id":"https://openalex.org/keywords/matroid-partitioning","display_name":"Matroid partitioning","score":0.5526889562606812},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5177894830703735},{"id":"https://openalex.org/keywords/oriented-matroid","display_name":"Oriented matroid","score":0.49198195338249207},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4143967926502228},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05542752146720886}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9872068166732788},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8824329376220703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8062717318534851},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7028824687004089},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.6417651176452637},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5891541242599487},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.5526889562606812},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5177894830703735},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.49198195338249207},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4143967926502228},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05542752146720886},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:re.public.polimi.it:11311/570333","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/570333","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.11575/cdm.v5i1.61894","is_oa":true,"landing_page_url":"https://doi.org/10.11575/cdm.v5i1.61894","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"mag:1573541561","is_oa":true,"landing_page_url":"https://cdm.ucalgary.ca/article/download/61894/46637","pdf_url":null,"source":{"id":"https://openalex.org/S2498033248","display_name":"Contributions to Discrete Mathematics","issn_l":"1715-0868","issn":["1715-0868"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310312896","host_organization_name":"University of Calgary Press","host_organization_lineage":["https://openalex.org/P4310312896"],"host_organization_lineage_names":["University of Calgary Press"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Contributions to Discrete Mathematics","raw_type":null}],"best_oa_location":{"id":"doi:10.11575/cdm.v5i1.61894","is_oa":true,"landing_page_url":"https://doi.org/10.11575/cdm.v5i1.61894","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1487262857","https://openalex.org/W1975978423","https://openalex.org/W1979134936","https://openalex.org/W2084562801","https://openalex.org/W2151201250"],"related_works":["https://openalex.org/W2034535646","https://openalex.org/W3140412805","https://openalex.org/W2206386752","https://openalex.org/W2991429782","https://openalex.org/W2894550712","https://openalex.org/W2157999380","https://openalex.org/W2890986337","https://openalex.org/W2612973915","https://openalex.org/W2107144967","https://openalex.org/W2981554314","https://openalex.org/W2952817478","https://openalex.org/W1986951898","https://openalex.org/W2908657436","https://openalex.org/W2087263470","https://openalex.org/W2086660922","https://openalex.org/W2027057754","https://openalex.org/W1967267296","https://openalex.org/W2265471685","https://openalex.org/W2596121192","https://openalex.org/W2005661925"],"abstract_inverted_index":{"Let":[0],"$M":[1],"=":[2],"(E,":[3],"\\mathcal{F})$":[4],"be":[5,68],"a":[6,9,75,92,98],"matroid":[7,77,94,100],"on":[8,78],"set":[10,20,63],"$E$":[11,50],"and":[12,82,113,129],"$B$":[13,29,109],"one":[14],"of":[15,42,46,49,71,74,110,120,136],"its":[16],"bases.":[17],"A":[18],"closed":[19,61],"$\\theta":[21],"\\subseteq":[22],"E$":[23],"is":[24,39,102,117,133],"saturated":[25,62],"with":[26,148],"respect":[27,149],"to":[28,67,97,104,146,150],"when":[30],"$|\\theta":[31],"\\cap":[32,55],"B":[33],"|":[34],"\\leq":[35,57],"r(\\theta)$,":[36],"where":[37],"$r(\\theta)$":[38],"the":[40,69],"rank":[41],"$\\theta$.":[43],"The":[44],"collection":[45],"subsets":[47],"$I$":[48],"such":[51],"that":[52,91],"$|":[53],"I":[54],"\\theta|":[56],"r(\\theta)$":[58],"for":[59,106],"every":[60,107],"$\\theta$":[64],"turns":[65],"out":[66],"family":[70],"independent":[72],"sets":[73],"new":[76],"$E$,":[79],"called":[80],"base-matroid":[81],"denoted":[83],"by":[84],"$M_B$.":[85],"In":[86],"this":[87],"paper":[88],"we":[89,139],"prove":[90],"graphic":[93,122],"$M$,":[95,111],"isomorphic":[96,103,145],"cycle":[99],"$M(G)$,":[101],"$M_B$,":[105,147],"base":[108,153],"if":[112,115,128,131],"only":[114,130],"$M$":[116,144],"direct":[118],"sum":[119],"uniform":[121],"matroids":[123,143],"or,":[124],"in":[125],"equivalent":[126],"way,":[127],"$G$":[132],"disjoint":[134],"union":[135],"cacti.":[137],"Moreover":[138],"characterize":[140],"simple":[141],"binary":[142],"an":[151],"assigned":[152],"$B$.":[154]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
