{"id":"https://openalex.org/W1515057391","doi":"https://doi.org/10.37236/3994","title":"Fan-Extensions in Fragile Matroids","display_name":"Fan-Extensions in Fragile Matroids","publication_year":2015,"publication_date":"2015-05-22","ids":{"openalex":"https://openalex.org/W1515057391","doi":"https://doi.org/10.37236/3994","mag":"1515057391"},"language":"en","primary_location":{"id":"doi:10.37236/3994","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3994","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p30/pdf","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://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p30/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041298817","display_name":"Carolyn Chun","orcid":"https://orcid.org/0000-0002-1872-8951"},"institutions":[{"id":"https://openalex.org/I59433898","display_name":"Brunel University of London","ror":"https://ror.org/00dn4t376","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I59433898"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Carolyn Chun","raw_affiliation_strings":["Brunel University","*Brunel University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Brunel University","institution_ids":["https://openalex.org/I59433898"]},{"raw_affiliation_string":"*Brunel University","institution_ids":["https://openalex.org/I59433898"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109408547","display_name":"Deborah Chun","orcid":null},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deborah Chun","raw_affiliation_strings":["West Virginia University","West Virginia University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"West Virginia University","institution_ids":["https://openalex.org/I12097938"]},{"raw_affiliation_string":"West Virginia University ,","institution_ids":["https://openalex.org/I12097938"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050651276","display_name":"Dillon Mayhew","orcid":"https://orcid.org/0000-0003-4086-0980"},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Dillon Mayhew","raw_affiliation_strings":["Victoria University of Wellington","(Victoria University of Wellington)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Victoria University of Wellington","institution_ids":["https://openalex.org/I41156924"]},{"raw_affiliation_string":"(Victoria University of Wellington)","institution_ids":["https://openalex.org/I41156924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046528024","display_name":"Stefan H. M. van Zwam","orcid":null},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stefan H. M. Van Zwam","raw_affiliation_strings":["Louisiana State University","Louisiana State University**"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Louisiana State University","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"Louisiana State University**","institution_ids":["https://openalex.org/I121820613"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4537,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82185243,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"22","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":0.9995999932289124,"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":0.9995999932289124,"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":0.9908000230789185,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9815000295639038,"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":0.9916608333587646},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8337491750717163},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.8262169361114502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7402592897415161},{"id":"https://openalex.org/keywords/backslash","display_name":"Backslash","score":0.7198784947395325},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5426403284072876},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.429876446723938},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41472500562667847},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09365701675415039},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.06312888860702515}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9916608333587646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8337491750717163},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.8262169361114502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7402592897415161},{"id":"https://openalex.org/C2780345915","wikidata":"https://www.wikidata.org/wiki/Q11185","display_name":"Backslash","level":2,"score":0.7198784947395325},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5426403284072876},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.429876446723938},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41472500562667847},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09365701675415039},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.06312888860702515},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/3994","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3994","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p30/pdf","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"},{"id":"pmh:oai:researchrepository.wvu.edu:faculty_publications-1162","is_oa":false,"landing_page_url":"https://researchrepository.wvu.edu/faculty_publications/163","pdf_url":null,"source":{"id":"https://openalex.org/S4306402612","display_name":"The Research Repository @ WVU (West Virginia University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I12097938","host_organization_name":"West Virginia University","host_organization_lineage":["https://openalex.org/I12097938"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty & Staff Scholarship","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.748.5113","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.748.5113","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1312.5401.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/3994","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3994","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p30/pdf","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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5400000214576721}],"awards":[{"id":"https://openalex.org/G5857988353","display_name":"Can we compare sets of points efficiently?","funder_award_id":"1501985","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337370","display_name":"Office of International Science and Engineering","ror":"https://ror.org/01k638r21"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1515057391.pdf","grobid_xml":"https://content.openalex.org/works/W1515057391.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W218653923","https://openalex.org/W1975424019","https://openalex.org/W1990364773","https://openalex.org/W2010114044","https://openalex.org/W2053279811","https://openalex.org/W2068183348","https://openalex.org/W2117933520","https://openalex.org/W2118686135","https://openalex.org/W2122667898","https://openalex.org/W2138805279","https://openalex.org/W2142728611","https://openalex.org/W2162598482","https://openalex.org/W2949938522","https://openalex.org/W6600980017","https://openalex.org/W6677879492"],"related_works":["https://openalex.org/W2949471446","https://openalex.org/W2058489697","https://openalex.org/W2106412416","https://openalex.org/W2068854468","https://openalex.org/W2952817478","https://openalex.org/W4297851595","https://openalex.org/W2118686135","https://openalex.org/W4300453872","https://openalex.org/W4313680207","https://openalex.org/W2951684632"],"abstract_inverted_index":{"If":[0],"$\\mathcal{S}$":[1],"is":[2,11,51,87],"a":[3,29,52,70,96],"set":[4],"of":[5,31,43,55,64,80],"matroids,":[6,57],"then":[7,90],"the":[8,61,78,88],"matroid":[9],"$M$":[10],"$\\mathcal{S}$-fragile":[12,56],"if,":[13],"for":[14],"every":[15],"element":[16],"$e\\in":[17],"E(M)$,":[18],"either":[19],"$M\\backslash":[20],"e$":[21],"or":[22,38],"$M/e$":[23],"has":[24],"no":[25],"minor":[26,71],"isomorphic":[27],"to":[28],"member":[30],"$\\mathcal{S}$.":[32],"Excluded-minor":[33],"characterizations":[34],"often":[35],"depend,":[36],"implicitly":[37],"explicitly,":[39],"on":[40],"understanding":[41],"classes":[42],"fragile":[44],"matroids.":[45],"In":[46],"certain":[47],"cases,":[48],"when":[49],"$\\mathcal{M}$":[50,65],"minor-closed":[53],"class":[54],"and":[58],"$N\\in":[59],"\\mathcal{M}$,":[60],"only":[62],"members":[63],"that":[66,84,104],"contain":[67],"$N$":[68,75],"as":[69],"are":[72,105],"obtained":[73],"from":[74],"by":[76],"increasing":[77],"length":[79],"fans.":[81],"We":[82],"prove":[83],"if":[85],"this":[86],"case,":[89],"we":[91],"can":[92],"certify":[93],"it":[94],"with":[95],"finite":[97],"case-analysis.":[98],"The":[99],"analysis":[100],"involves":[101],"examining":[102],"matroids":[103],"at":[106],"most":[107],"two":[108],"elements":[109],"larger":[110],"than":[111],"$N$.":[112]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
