{"id":"https://openalex.org/W2963031626","doi":"https://doi.org/10.37236/5937","title":"Isotropic Matroids III: Connectivity","display_name":"Isotropic Matroids III: Connectivity","publication_year":2017,"publication_date":"2017-06-30","ids":{"openalex":"https://openalex.org/W2963031626","doi":"https://doi.org/10.37236/5937","mag":"2963031626"},"language":"en","primary_location":{"id":"doi:10.37236/5937","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5937","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/5937","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057971093","display_name":"Robert Brijder","orcid":"https://orcid.org/0000-0002-8912-1735"},"institutions":[{"id":"https://openalex.org/I878454856","display_name":"Hasselt University","ror":"https://ror.org/04nbhqj75","country_code":"BE","type":"education","lineage":["https://openalex.org/I878454856"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Robert Brijder","raw_affiliation_strings":["Hasselt University and Transnational University of Limburg"],"affiliations":[{"raw_affiliation_string":"Hasselt University and Transnational University of Limburg","institution_ids":["https://openalex.org/I878454856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066749771","display_name":"Lorenzo Traldi","orcid":"https://orcid.org/0000-0003-1097-2818"},"institutions":[{"id":"https://openalex.org/I184759092","display_name":"Lafayette College","ror":"https://ror.org/036n0x007","country_code":"US","type":"education","lineage":["https://openalex.org/I184759092"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lorenzo Traldi","raw_affiliation_strings":["Lafayette College"],"affiliations":[{"raw_affiliation_string":"Lafayette College","institution_ids":["https://openalex.org/I184759092"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057971093"],"corresponding_institution_ids":["https://openalex.org/I878454856"],"apc_list":null,"apc_paid":null,"fwci":0.2271,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60507752,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.934768557548523},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.7736608982086182},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7373353242874146},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7265137434005737},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.643609344959259},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4794808328151703},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34135323762893677},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23061877489089966},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07894861698150635}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.934768557548523},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.7736608982086182},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7373353242874146},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7265137434005737},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.643609344959259},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4794808328151703},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34135323762893677},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23061877489089966},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07894861698150635}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/5937","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5937","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/5937","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5937","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1515707356","https://openalex.org/W1963490734","https://openalex.org/W1984509778","https://openalex.org/W1990600049","https://openalex.org/W1992797912","https://openalex.org/W2009306025","https://openalex.org/W2015381896","https://openalex.org/W2017608048","https://openalex.org/W2022922394","https://openalex.org/W2026944308","https://openalex.org/W2038711832","https://openalex.org/W2059123040","https://openalex.org/W2106818977","https://openalex.org/W2914422925"],"related_works":["https://openalex.org/W2058299944","https://openalex.org/W4323360720","https://openalex.org/W1550144461","https://openalex.org/W4233892543","https://openalex.org/W2783959783","https://openalex.org/W2602164040","https://openalex.org/W2037206237","https://openalex.org/W4310658774","https://openalex.org/W3000635646","https://openalex.org/W2381226549"],"abstract_inverted_index":{"The":[0],"isotropic":[1,17,33,36,42],"matroid":[2],"$M[IAS(G)]$":[3,64,86,120],"of":[4,29,53,78,105,146],"a":[5,9,99,103,141,144],"graph":[6,142],"$G$":[7,57,72,93,115,136],"is":[8,13,48,65,73,87,94,112,121,128,137],"binary":[10],"matroid,":[11],"which":[12],"equivalent":[14,49,129,139],"to":[15,32,50,130,140],"the":[16,41,76,131],"system":[18,43],"introduced":[19],"by":[20,46],"Bouchet.":[21],"In":[22],"this":[23],"paper":[24],"we":[25],"discuss":[26],"four":[27,61],"notions":[28],"connectivity":[30,44,52],"related":[31],"matroids":[34],"and":[35,55,69,90,96],"systems.":[37],"We":[38,82],"show":[39,84],"that":[40,85,113,135],"defined":[45],"Bouchet":[47],"vertical":[51],"$M[IAS(G)]$,":[54],"if":[56,68,71,89,92,114],"has":[58,97,116],"at":[59],"least":[60],"vertices,":[62],"then":[63,119],"vertically":[66,123],"5-connected":[67],"only":[70,91],"prime":[74],"(in":[75],"sense":[77],"Cunningham's":[79],"split":[80],"decomposition).":[81],"also":[83],"$3$-connected":[88],"connected":[95],"neither":[98],"pendant":[100],"vertex":[101,145],"nor":[102],"pair":[104],"twin":[106],"vertices.":[107],"Our":[108],"most":[109],"interesting":[110],"theorem":[111],"$n\\geq7$":[117],"vertices":[118],"not":[122],"$n$-connected.":[124],"This":[125],"abstract-seeming":[126],"result":[127],"more":[132],"concrete":[133],"assertion":[134],"locally":[138],"with":[143],"degree":[147],"$<\\frac{n-1}{2}$.":[148]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}