{"id":"https://openalex.org/W3035698984","doi":"https://doi.org/10.37236/9653","title":"Diameters of Cocircuit Graphs of Oriented Matroids: An Update","display_name":"Diameters of Cocircuit Graphs of Oriented Matroids: An Update","publication_year":2021,"publication_date":"2021-12-03","ids":{"openalex":"https://openalex.org/W3035698984","doi":"https://doi.org/10.37236/9653","mag":"3035698984"},"language":"en","primary_location":{"id":"doi:10.37236/9653","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9653","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p40/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/v28i4p40/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113318292","display_name":"Ilan Adler","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ilan Adler","raw_affiliation_strings":["Dept. of Industrial Engineering and Operations Research, Univ. of California, Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Industrial Engineering and Operations Research, Univ. of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055755657","display_name":"Jes\u00fas A. De Loera","orcid":"https://orcid.org/0000-0002-9556-1112"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jes\u00fas A. De Loera","raw_affiliation_strings":["Department of Mathematics, Univ. of California, Davis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Univ. of California, Davis","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056971666","display_name":"Steven Klee","orcid":null},"institutions":[{"id":"https://openalex.org/I58610484","display_name":"Seattle University","ror":"https://ror.org/02jqc0m91","country_code":"US","type":"education","lineage":["https://openalex.org/I58610484"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven Klee","raw_affiliation_strings":["Department of Mathematics, Seattle University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Seattle University","institution_ids":["https://openalex.org/I58610484"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101596698","display_name":"Zhenyang Zhang","orcid":"https://orcid.org/0009-0000-2821-7736"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhenyang Zhang","raw_affiliation_strings":["Department of Mathematics, Univ. of California, Davis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Univ. of California, Davis","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.002076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9983999729156494,"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":0.9983999729156494,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9919999837875366,"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":0.9813997149467468},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7765865325927734},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6927942037582397},{"id":"https://openalex.org/keywords/graphic-matroid","display_name":"Graphic matroid","score":0.6073582172393799},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5950139760971069},{"id":"https://openalex.org/keywords/matroid-partitioning","display_name":"Matroid partitioning","score":0.5577455759048462},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5246617794036865},{"id":"https://openalex.org/keywords/oriented-matroid","display_name":"Oriented matroid","score":0.4383249580860138},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36966702342033386}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9813997149467468},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7765865325927734},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6927942037582397},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.6073582172393799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5950139760971069},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.5577455759048462},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5246617794036865},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.4383249580860138},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36966702342033386}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9653","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9653","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p40/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"}],"best_oa_location":{"id":"doi:10.37236/9653","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9653","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i4p40/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":[],"awards":[{"id":"https://openalex.org/G3355331909","display_name":null,"funder_award_id":"1818969","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3925616921","display_name":"RUI: Structural and enumerative problems on simplicial complexes","funder_award_id":"1600048","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4797998838","display_name":null,"funder_award_id":"DMS-1600048","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G565295993","display_name":null,"funder_award_id":"CCF-1934568","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7096521375","display_name":null,"funder_award_id":"DMS-1818969","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/F4320336197","display_name":"Tsinghua-Berkeley Shenzhen institute","ror":"https://ror.org/02hhwwz98"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3035698984.pdf","grobid_xml":"https://content.openalex.org/works/W3035698984.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W276224435","https://openalex.org/W1494570670","https://openalex.org/W1546808752","https://openalex.org/W1591912906","https://openalex.org/W1594139983","https://openalex.org/W1762430620","https://openalex.org/W1963547452","https://openalex.org/W1965826347","https://openalex.org/W1966068899","https://openalex.org/W1982231437","https://openalex.org/W2008722267","https://openalex.org/W2033342930","https://openalex.org/W2050088862","https://openalex.org/W2058299944","https://openalex.org/W2062061242","https://openalex.org/W2080798818","https://openalex.org/W2093344147","https://openalex.org/W2094525238","https://openalex.org/W2117921017","https://openalex.org/W2151888904","https://openalex.org/W2160442375","https://openalex.org/W2165204638","https://openalex.org/W2304796618","https://openalex.org/W2592711915","https://openalex.org/W2809374263","https://openalex.org/W2949373715","https://openalex.org/W2971330320","https://openalex.org/W3102625362","https://openalex.org/W3102921527","https://openalex.org/W3103462803","https://openalex.org/W3105031228","https://openalex.org/W4206570602","https://openalex.org/W4212938248","https://openalex.org/W4254205555","https://openalex.org/W4301808069"],"related_works":["https://openalex.org/W2400862597","https://openalex.org/W2058489697","https://openalex.org/W2072414647","https://openalex.org/W1984819493","https://openalex.org/W2159059797","https://openalex.org/W2625145881","https://openalex.org/W4246417054","https://openalex.org/W2550106438","https://openalex.org/W2006784845","https://openalex.org/W4226057593"],"abstract_inverted_index":{"Oriented":[0,19],"matroids":[1,20,86,102,113,168,182],"are":[2,203],"combinatorial":[3],"structures":[4],"that":[5,146],"generalize":[6],"point":[7],"configurations,":[8,10],"vector":[9],"hyperplane":[11],"arrangements,":[12],"polyhedra,":[13],"linear":[14,149],"programs,":[15],"and":[16,30,37,69,78,106,109,172],"directed":[17],"graphs.":[18],"have":[21],"played":[22],"a":[23,122,135,148],"key":[24],"role":[25],"in":[26],"combinatorics,":[27],"computational":[28],"geometry,":[29],"optimization.":[31],"This":[32],"paper":[33],"surveys":[34],"prior":[35],"work":[36],"presents":[38],"an":[39,54,132,143],"update":[40],"on":[41,46],"the":[42,47,50,63,66,70,75,80,96,152,157,162,189,200],"search":[43,194],"for":[44,59,100,110,151,166,179],"bounds":[45,82,99],"diameter":[48,76,81,153],"of":[49,53,65,83,90,103,138,169,199],"cocircuit":[51],"graph":[52],"oriented":[55,85,92,101,112,128,167,181],"matroid.":[56],"The":[57],"motivation":[58],"our":[60,192],"investigations":[61],"is":[62,154,164],"complexity":[64],"simplex":[67],"method":[68],"criss-cross":[71],"method.&#x0D;":[72],"We":[73,94],"review":[74],"problem":[77],"show":[79,161],"general":[84],"reduce":[87],"to":[88,116,134,185],"those":[89],"uniform":[91],"matroids.":[93],"give":[95],"latest":[97],"exact":[98],"low":[104,107,170,173],"rank":[105,171],"corank,":[108,174],"all":[111,180],"with":[114,177,183],"up":[115,184],"nine":[117,186],"elements":[118],"(this":[119],"part":[120],"required":[121],"large":[123],"computer-based":[124],"proof).":[125],"For":[126],"arbitrary":[127],"matroids,":[129],"we":[130,160],"present":[131],"improvement":[133],"quadratic":[136],"bound":[137,150],"Finschi.":[139],"Our":[140],"discussion":[141],"highlights":[142],"old":[144],"conjecture":[145,163,202],"states":[147],"possible.":[155],"On":[156,188],"positive":[158],"side,":[159,191],"true":[165],"and,":[175],"verified":[176],"computers,":[178],"elements.":[187],"negative":[190],"computer":[193],"showed":[195],"two":[196],"natural":[197],"strengthenings":[198],"main":[201],"false.":[204]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
