{"id":"https://openalex.org/W2043377474","doi":"https://doi.org/10.1137/090759616","title":"An Obstacle to a Decomposition Theorem for Near-Regular Matroids","display_name":"An Obstacle to a Decomposition Theorem for Near-Regular Matroids","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2043377474","doi":"https://doi.org/10.1137/090759616","mag":"2043377474"},"language":"en","primary_location":{"id":"doi:10.1137/090759616","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090759616","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050651276","display_name":"Dillon Mayhew","orcid":"https://orcid.org/0000-0003-4086-0980"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dillon Mayhew","raw_affiliation_strings":["Dillon.Mayhew@msor.vuw.ac.nz and Geoff.Whittle@msor.vuw.ac.nz#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dillon.Mayhew@msor.vuw.ac.nz and Geoff.Whittle@msor.vuw.ac.nz#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019046311","display_name":"Geoff Whittle","orcid":null},"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":"Geoff Whittle","raw_affiliation_strings":["(Victoria University of Wellington)"],"raw_orcid":null,"affiliations":[{"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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan H. M. van Zwam","raw_affiliation_strings":["Stefan.van.Zwam@cwi.nl#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stefan.van.Zwam@cwi.nl#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8109,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.75895313,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"25","issue":"1","first_page":"271","last_page":"279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9944999814033508,"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/T11130","display_name":"Coding theory and cryptography","score":0.9754999876022339,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9915397763252258},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.8089050054550171},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7667958736419678},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7312434315681458},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5927284955978394},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49741461873054504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13192793726921082}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9915397763252258},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.8089050054550171},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7667958736419678},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7312434315681458},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5927284955978394},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49741461873054504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13192793726921082},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090759616","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090759616","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W141699115","https://openalex.org/W1840565821","https://openalex.org/W1963547452","https://openalex.org/W1964953074","https://openalex.org/W1967097051","https://openalex.org/W1973734662","https://openalex.org/W1997357497","https://openalex.org/W2010114044","https://openalex.org/W2020328701","https://openalex.org/W2040101882","https://openalex.org/W2064723091","https://openalex.org/W2068049130","https://openalex.org/W2081802266","https://openalex.org/W2118686135","https://openalex.org/W2138805279","https://openalex.org/W2143602504","https://openalex.org/W2182109708","https://openalex.org/W2490322923","https://openalex.org/W3100204681","https://openalex.org/W4210751359"],"related_works":["https://openalex.org/W2058489697","https://openalex.org/W2106412416","https://openalex.org/W4367050287","https://openalex.org/W2046319394","https://openalex.org/W146649319","https://openalex.org/W2072414647","https://openalex.org/W2550106438","https://openalex.org/W4313680207","https://openalex.org/W2494200571","https://openalex.org/W2409819057"],"abstract_inverted_index":{"Seymour's":[0],"decomposition":[1],"theorem":[2],"[J.":[3],"Combin.":[4],"Theory":[5],"Ser.":[6],"B,":[7],"28":[8],"(1980),":[9],"pp.":[10],"305\u2013359]":[11],"for":[12,50,56],"regular":[13],"matroids":[14,29,66,71],"states":[15],"that":[16,30,46,63,72,83,108],"any":[17],"matroid":[18],"representable":[19],"over":[20],"both":[21],"$\\mathrm{GF}(2)$":[22],"and":[23,41],"$\\mathrm{GF}(3)$":[24],"can":[25,67],"be":[26,68],"obtained":[27,69],"from":[28,70],"are":[31,87],"graphic,":[32],"cographic,":[33],"or":[34],"isomorphic":[35],"to":[36,74],"$R_{10}$":[37],"by":[38],"1-,":[39],"2-,":[40],"3-sums.":[42],"It":[43],"is":[44],"hoped":[45],"similar":[47],"characterizations":[48],"hold":[49],"other":[51],"classes":[52,78,86],"of":[53,59],"matroids,":[54,96],"notably":[55],"the":[57],"class":[58,92],"near-regular":[60,65],"matroids.":[61,103],"Suppose":[62],"all":[64,94,101],"belong":[73],"a":[75,91],"few":[76],"basic":[77,85],"through":[79],"k-sums.":[80],"Also":[81],"suppose":[82],"these":[84],"such":[88],"that,":[89,106],"whenever":[90],"contains":[93],"graphic":[95],"it":[97],"does":[98],"not":[99,112],"contain":[100],"cographic":[102],"We":[104],"show":[105],"in":[107],"case,":[109],"3-sums":[110],"will":[111],"suffice.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}