{"id":"https://openalex.org/W1514518893","doi":"https://doi.org/10.37236/1773","title":"Goldberg-Coxeter Construction for $3$- and $4$-valent Plane Graphs","display_name":"Goldberg-Coxeter Construction for $3$- and $4$-valent Plane Graphs","publication_year":2004,"publication_date":"2004-03-05","ids":{"openalex":"https://openalex.org/W1514518893","doi":"https://doi.org/10.37236/1773","mag":"1514518893"},"language":"en","primary_location":{"id":"doi:10.37236/1773","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1773","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r20/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":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":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032090330","display_name":"Mathieu Dutour Sikiri\u0107","orcid":"https://orcid.org/0000-0001-7641-4785"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]},{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["FR","IL","JP"],"is_corresponding":true,"raw_author_name":"Mathieu Dutour","raw_affiliation_strings":["LIGA, ENS/CNRS, Paris and","LIGA, ENS/CNRS, Paris and Hebrew University, Jerusalem","Institute of Statistical Mathematics, Tokyo"],"affiliations":[{"raw_affiliation_string":"LIGA, ENS/CNRS, Paris and","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIGA, ENS/CNRS, Paris and Hebrew University, Jerusalem","institution_ids":["https://openalex.org/I197251160","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Institute of Statistical Mathematics, Tokyo","institution_ids":["https://openalex.org/I4210134673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113871341","display_name":"Michel Deza","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]},{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["FR","IL","JP"],"is_corresponding":false,"raw_author_name":"Michel Deza","raw_affiliation_strings":["LIGA, ENS/CNRS, Paris and","Institute of Statistical Mathematics, Tokyo","LIGA, ENS/CNRS, Paris and Hebrew University, Jerusalem"],"affiliations":[{"raw_affiliation_string":"LIGA, ENS/CNRS, Paris and","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Institute of Statistical Mathematics, Tokyo","institution_ids":["https://openalex.org/I4210134673"]},{"raw_affiliation_string":"LIGA, ENS/CNRS, Paris and Hebrew University, Jerusalem","institution_ids":["https://openalex.org/I197251160","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032090330"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I197251160","https://openalex.org/I4210134673"],"apc_list":null,"apc_paid":null,"fwci":1.5511,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.77847794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"1","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":0.9998000264167786,"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":0.9998000264167786,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9965000152587891,"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/T11476","display_name":"Graph theory and applications","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/combinatorics","display_name":"Combinatorics","score":0.7897235155105591},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7713049650192261},{"id":"https://openalex.org/keywords/coxeter-group","display_name":"Coxeter group","score":0.669587254524231},{"id":"https://openalex.org/keywords/coxeter-graph","display_name":"Coxeter graph","score":0.5307626128196716},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4508393704891205},{"id":"https://openalex.org/keywords/zigzag","display_name":"Zigzag","score":0.44251179695129395},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4130937457084656},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3961418569087982},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.2448677122592926},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22932228446006775},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.22871723771095276}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7897235155105591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7713049650192261},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.669587254524231},{"id":"https://openalex.org/C27225450","wikidata":"https://www.wikidata.org/wiki/Q3115477","display_name":"Coxeter graph","level":5,"score":0.5307626128196716},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4508393704891205},{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.44251179695129395},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4130937457084656},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3961418569087982},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.2448677122592926},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22932228446006775},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.22871723771095276}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/1773","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1773","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r20/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":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:10.1.1.4.8327","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.8327","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_11/PDF/v11i1r20.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1773","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1773","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r20/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":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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1514518893.pdf","grobid_xml":"https://content.openalex.org/works/W1514518893.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W92252332","https://openalex.org/W1538279012","https://openalex.org/W1582748983","https://openalex.org/W1852326543","https://openalex.org/W1966134672","https://openalex.org/W1967678995","https://openalex.org/W1974569474","https://openalex.org/W1976287241","https://openalex.org/W1997672782","https://openalex.org/W2008641168","https://openalex.org/W2012909180","https://openalex.org/W2013761912","https://openalex.org/W2019424330","https://openalex.org/W2050321546","https://openalex.org/W2078507839","https://openalex.org/W2090361723","https://openalex.org/W2093295848","https://openalex.org/W2164162886","https://openalex.org/W2204909750","https://openalex.org/W2329714975","https://openalex.org/W2498830265","https://openalex.org/W2510708339","https://openalex.org/W2911722782","https://openalex.org/W3022636055","https://openalex.org/W3175367423","https://openalex.org/W4253797498","https://openalex.org/W4388288416","https://openalex.org/W4394653775"],"related_works":["https://openalex.org/W2949181670","https://openalex.org/W2084129846","https://openalex.org/W2949874136","https://openalex.org/W1975064256","https://openalex.org/W1520548203","https://openalex.org/W4300406539","https://openalex.org/W2418172795","https://openalex.org/W2121475343","https://openalex.org/W4299394022","https://openalex.org/W1606013690"],"abstract_inverted_index":{"We":[0,99,134],"consider":[1,148],"the":[2,13,71,96,101,108,112,116,119,131,137],"Goldberg-Coxeter":[3],"construction":[4],"$GC_{k,l}(G_0)$":[5,146],"(a":[6],"generalization":[7],"of":[8,12,28,58,86,107,115,126,140,145],"a":[9,35,52,56,74,78,84,122],"simplicial":[10],"subdivision":[11],"dodecahedron":[14],"considered":[15],"by":[16,152],"Goldberg":[17],"[Tohoku":[18],"Mathematical":[19],"Journal,":[20],"43":[21],"(1937)":[22],"104\u2013108]":[23],"and":[24,121,147],"Coxeter":[25],"[A":[26],"Spectrum":[27],"Mathematics,":[29],"OUP,":[30],"(1971)":[31],"98\u2013107]),":[32],"which":[33],"produces":[34],"plane":[36,43,53,80],"graph":[37,44,54,81,110],"from":[38],"any":[39,62],"$3$-":[40],"or":[41],"$4$-valent":[42,79],"for":[45],"integer":[46],"parameters":[47],"$k,l$.":[48],"A":[49],"zigzag":[50,102],"in":[51,77],"is":[55,83],"circuit":[57,76,85],"edges,":[59,87],"such":[60,88],"that":[61,89],"two,":[63],"but":[64,155],"no":[65,90],"three,":[66],"consecutive":[67,92],"edges":[68,93],"belong":[69,94],"to":[70,95],"same":[72,97],"face;":[73],"central":[75,104,143,159],"$G$":[82],"two":[91],"face.":[98],"study":[100,136],"(or":[103,142,158],"circuit)":[105],"structure":[106],"resulting":[109],"using":[111],"algebraic":[113],"formalism":[114],"moving":[117],"group,":[118],"$(k,l)$-product":[120],"finite":[123],"index":[124],"subgroup":[125],"$SL_2(\\Bbb{Z})$,":[127],"whose":[128],"elements":[129],"preserve":[130],"above":[132],"structure.":[133],"also":[135],"intersection":[138],"pattern":[139],"zigzags":[141,157],"circuits)":[144],"its":[149],"projections,":[150],"obtained":[151],"removing":[153],"all":[154],"one":[156],"circuits).":[160]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
