{"id":"https://openalex.org/W3024548395","doi":"https://doi.org/10.37236/10374","title":"Minimum Number of Edges of Polytopes with $2d+2$ Vertices","display_name":"Minimum Number of Edges of Polytopes with $2d+2$ Vertices","publication_year":2022,"publication_date":"2022-07-14","ids":{"openalex":"https://openalex.org/W3024548395","doi":"https://doi.org/10.37236/10374","mag":"3024548395"},"language":"en","primary_location":{"id":"doi:10.37236/10374","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10374","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i3p18/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/v29i3p18/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044609877","display_name":"Guillermo Pineda\u2010Villavicencio","orcid":"https://orcid.org/0000-0002-2904-6657"},"institutions":[{"id":"https://openalex.org/I149704539","display_name":"Deakin University","ror":"https://ror.org/02czsnj07","country_code":"AU","type":"education","lineage":["https://openalex.org/I149704539"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Guillermo Pineda-Villavicencio","raw_affiliation_strings":["Deakin University"],"affiliations":[{"raw_affiliation_string":"Deakin University","institution_ids":["https://openalex.org/I149704539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059687109","display_name":"Julien Ugon","orcid":"https://orcid.org/0000-0001-5290-8051"},"institutions":[{"id":"https://openalex.org/I149704539","display_name":"Deakin University","ror":"https://ror.org/02czsnj07","country_code":"AU","type":"education","lineage":["https://openalex.org/I149704539"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Julien Ugon","raw_affiliation_strings":["Deakin University"],"affiliations":[{"raw_affiliation_string":"Deakin University","institution_ids":["https://openalex.org/I149704539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017442299","display_name":"David Yost","orcid":"https://orcid.org/0000-0003-2275-8579"},"institutions":[{"id":"https://openalex.org/I149672521","display_name":"Federation University","ror":"https://ror.org/05qbzwv83","country_code":"AU","type":"education","lineage":["https://openalex.org/I149672521"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"David Yost","raw_affiliation_strings":["Federation University"],"affiliations":[{"raw_affiliation_string":"Federation University","institution_ids":["https://openalex.org/I149672521"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044609877"],"corresponding_institution_ids":["https://openalex.org/I149704539"],"apc_list":null,"apc_paid":null,"fwci":1.1371,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.67372737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991000294685364,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9932000041007996,"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/polytope","display_name":"Polytope","score":0.9019573926925659},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.880616307258606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.800613522529602},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5762574076652527},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.5608072876930237},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43516767024993896},{"id":"https://openalex.org/keywords/wedge","display_name":"Wedge (geometry)","score":0.4165910482406616},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1239950954914093}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9019573926925659},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.880616307258606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.800613522529602},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5762574076652527},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.5608072876930237},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43516767024993896},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.4165910482406616},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1239950954914093}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/10374","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10374","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i3p18/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:vital:17606","is_oa":true,"landing_page_url":"http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/190357","pdf_url":null,"source":{"id":"https://openalex.org/S4306400234","display_name":"FedUni ResearchOnline (Federation University Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210158496","host_organization_name":"Australian Federation of University Women \u2013 South Australia","host_organization_lineage":["https://openalex.org/I4210158496"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:vital:19319","is_oa":true,"landing_page_url":"http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/200083","pdf_url":null,"source":{"id":"https://openalex.org/S4306400234","display_name":"FedUni ResearchOnline (Federation University Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210158496","host_organization_name":"Australian Federation of University Women \u2013 South Australia","host_organization_lineage":["https://openalex.org/I4210158496"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:dro.deakin.edu.au:DU:30175906","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401102","display_name":"Own your potential (DEAKIN)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149704539","host_organization_name":"Deakin University","host_organization_lineage":["https://openalex.org/I149704539"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:figshare.com:article/21131446","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Minimum_Number_of_Edges_of_Polytopes_with_2d_2_Vertices/21131446","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.37236/10374","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10374","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i3p18/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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3024548395.pdf","grobid_xml":"https://content.openalex.org/works/W3024548395.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1597196612","https://openalex.org/W1976896880","https://openalex.org/W1996522633","https://openalex.org/W2031806265","https://openalex.org/W2053179523","https://openalex.org/W2053580980","https://openalex.org/W2068162092","https://openalex.org/W2070124018","https://openalex.org/W2121123998","https://openalex.org/W2271061143","https://openalex.org/W2587167237","https://openalex.org/W2605255283","https://openalex.org/W2613641366","https://openalex.org/W2963693207","https://openalex.org/W3130258882","https://openalex.org/W3192935815","https://openalex.org/W4238176006","https://openalex.org/W4298392872"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2507185596","https://openalex.org/W1493684871","https://openalex.org/W4286224459","https://openalex.org/W2886567582","https://openalex.org/W4289703404","https://openalex.org/W4387265813","https://openalex.org/W3103454236","https://openalex.org/W4286870264","https://openalex.org/W2994911322"],"abstract_inverted_index":{"We":[0,22,45],"define":[1],"two":[2],"$d$-polytopes,":[3],"both":[4],"with":[5,38],"$2d+2$":[6,39],"vertices":[7],"and":[8,16],"$(d+3)(d-1)$":[9],"edges,":[10,34],"which":[11],"reduce":[12],"to":[13],"the":[14,17,27,31,48],"cube":[15],"5-wedge":[18],"in":[19],"dimension":[20],"three.":[21],"show":[23],"that":[24],"they":[25],"are":[26],"only":[28],"minimisers":[29],"of":[30,33],"number":[32],"amongst":[35],"all":[36],"$d$-polytopes":[37],"vertices,":[40],"when":[41],"$d=6$":[42],"or":[43,54],"$d\\ge8$.":[44],"also":[46],"characterise":[47],"minimising":[49],"polytopes":[50],"for":[51],"$d=4,":[52],"5$":[53],"7,":[55],"where":[56],"four":[57],"sporadic":[58],"examples":[59],"arise.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
