{"id":"https://openalex.org/W1610395761","doi":"https://doi.org/10.37236/1648","title":"On the Excluded Minors for Matroids of Branch-Width Three","display_name":"On the Excluded Minors for Matroids of Branch-Width Three","publication_year":2002,"publication_date":"2002-07-23","ids":{"openalex":"https://openalex.org/W1610395761","doi":"https://doi.org/10.37236/1648","mag":"1610395761"},"language":"en","primary_location":{"id":"doi:10.37236/1648","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1648","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r32/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":false,"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":null,"license_id":null,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r32/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090886391","display_name":"Petr Hlin\u011bn\u00fd","orcid":"https://orcid.org/0000-0003-2125-1514"},"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":true,"raw_author_name":"Petr Hlin\u011bn\u00fd","raw_affiliation_strings":["Institute for Theoretical Computer Science \u2020 (ITI MFF), Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic","School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand;"],"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Computer Science \u2020 (ITI MFF), Charles University, Malostransk\u00e9 n\u00e1m. 25, 118 00 Praha 1, Czech Republic","institution_ids":[]},{"raw_affiliation_string":"School of Mathematical and Computing Sciences, Victoria University, P.O. Box 600, Wellington, New Zealand;","institution_ids":["https://openalex.org/I41156924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090886391"],"corresponding_institution_ids":["https://openalex.org/I41156924"],"apc_list":null,"apc_paid":null,"fwci":2.0991,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.86338592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"9","issue":"1","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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9947999715805054,"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":0.9898999929428101,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.9905422925949097},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.806241512298584},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8044446706771851},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7248611450195312},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.6303227543830872},{"id":"https://openalex.org/keywords/matroid-partitioning","display_name":"Matroid partitioning","score":0.615315854549408},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6136038303375244},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5672116875648499},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.5360363721847534},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.49457213282585144},{"id":"https://openalex.org/keywords/oriented-matroid","display_name":"Oriented matroid","score":0.44772887229919434},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4450984597206116},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4235786497592926},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15335649251937866},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07242050766944885}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9905422925949097},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.806241512298584},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8044446706771851},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7248611450195312},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.6303227543830872},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.615315854549408},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6136038303375244},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5672116875648499},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.5360363721847534},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.49457213282585144},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.44772887229919434},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4450984597206116},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4235786497592926},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15335649251937866},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07242050766944885},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1648","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1648","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r32/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.4.5389","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.5389","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PostScriptfiles/v9i1r32.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.4.9625","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.9625","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PDF/v9i1r32.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1648","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1648","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r32/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":false,"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":null,"license_id":null,"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":[{"id":"https://openalex.org/F4320335369","display_name":"Marsden Fund","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1610395761.pdf","grobid_xml":"https://content.openalex.org/works/W1610395761.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W169588220","https://openalex.org/W1610395761","https://openalex.org/W1987279762","https://openalex.org/W2006587062","https://openalex.org/W2040101882","https://openalex.org/W2047871605","https://openalex.org/W2067016370","https://openalex.org/W2070056858","https://openalex.org/W2079618965","https://openalex.org/W2163718580"],"related_works":["https://openalex.org/W2400862597","https://openalex.org/W2058489697","https://openalex.org/W2072414647","https://openalex.org/W1984819493","https://openalex.org/W2625145881","https://openalex.org/W2159059797","https://openalex.org/W4246417054","https://openalex.org/W2550106438","https://openalex.org/W2006784845","https://openalex.org/W2118686135"],"abstract_inverted_index":{"Knowing":[0],"the":[1],"excluded":[2,42],"minors":[3],"for":[4,44,99,127],"a":[5,10,74,95,101,105,117],"minor-closed":[6],"matroid":[7],"property":[8],"provides":[9],"useful":[11],"alternative":[12],"characterization":[13],"of":[14,32,46,69,85,104],"that":[15,37,59],"property.":[16],"It":[17],"has":[18,52],"been":[19],"shown":[20],"in":[21,79,109],"[R.":[22],"Hall,":[23],"J.":[24],"Oxley,":[25],"C.":[26],"Semple,":[27],"G.":[28],"Whittle,":[29],"On":[30],"Matroids":[31],"Branch-Width":[33],"Three,":[34],"submitted":[35],"2001]":[36],"if":[38],"$M$":[39,67],"is":[40],"an":[41],"minor":[43],"matroids":[45,66,90,143],"branch-width":[47],"$3$,":[48],"then":[49],"$":[50,91],"M$":[51],"at":[53,145],"most":[54,146],"$14$":[55,147],"elements.":[56,148],"We":[57,81],"show":[58],"there":[60],"are":[61,71,112],"exactly":[62],"$10$":[63],"such":[64,86],"binary":[65],"(7":[68],"which":[70],"regular),":[72],"proving":[73],"conjecture":[75],"formulated":[76],"by":[77],"Dharmatilake":[78],"1994.":[80],"also":[82],"construct":[83],"numbers":[84],"ternary":[87],"and":[88,93],"quaternary":[89],"M$,":[92],"provide":[94],"simple":[96],"practical":[97],"algorithm":[98],"finding":[100],"width-$3$":[102],"branch-decomposition":[103],"matroid.":[106],"The":[107,122],"arguments":[108],"our":[110],"paper":[111],"computer-assisted":[113],"\u2014":[114],"we":[115],"use":[116],"program":[118],"$MACEK$":[119],"[P.":[120],"Hlin\u011bn\u00fd,":[121],"MACEK":[123],"Program,":[124],"http://www.mcs.vuw.ac.nz/research/macek,":[125],"2002]":[126],"structural":[128],"computations":[129],"with":[130],"represented":[131],"matroids.":[132],"Unfortunately,":[133],"it":[134],"seems":[135],"to":[136,139],"be":[137],"infeasible":[138],"search":[140],"through":[141],"all":[142],"on":[144]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
