{"id":"https://openalex.org/W3005130258","doi":"https://doi.org/10.1002/jgt.22665","title":"Drawings of complete graphs in the projective plane","display_name":"Drawings of complete graphs in the projective plane","publication_year":2021,"publication_date":"2021-03-23","ids":{"openalex":"https://openalex.org/W3005130258","doi":"https://doi.org/10.1002/jgt.22665","mag":"3005130258"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.22665","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.22665","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2002.02287","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055821136","display_name":"Alan Arroyo","orcid":"https://orcid.org/0000-0003-2401-8670"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Alan Arroyo","raw_affiliation_strings":["IST Austria  Klosterneuburg Austria","IST Austria, Klosterneuburg, Austria"],"affiliations":[{"raw_affiliation_string":"IST Austria  Klosterneuburg Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"IST Austria, Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043769160","display_name":"Dan McQuillan","orcid":null},"institutions":[{"id":"https://openalex.org/I4210151403","display_name":"Norwich University Applied Research Institute","ror":"https://ror.org/05bqezz06","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210151403"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dan McQuillan","raw_affiliation_strings":["College of Science and Mathematics Norwich University  Northfield Vermont USA","College of Science and Mathematics, Norwich University, Northfield, Vermont, USA"],"affiliations":[{"raw_affiliation_string":"College of Science and Mathematics Norwich University  Northfield Vermont USA","institution_ids":["https://openalex.org/I4210151403"]},{"raw_affiliation_string":"College of Science and Mathematics, Norwich University, Northfield, Vermont, USA","institution_ids":["https://openalex.org/I4210151403"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034310573","display_name":"R. Bruce Richter","orcid":"https://orcid.org/0000-0002-1444-9699"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R. Bruce Richter","raw_affiliation_strings":["Department of Combinatorics and Optimization University of Waterloo  Waterloo Ontario Canada","Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization University of Waterloo  Waterloo Ontario Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060540226","display_name":"Gelasio Salazar","orcid":"https://orcid.org/0000-0002-8458-3930"},"institutions":[{"id":"https://openalex.org/I196664497","display_name":"Autonomous University of San Luis Potos\u00ed","ror":"https://ror.org/000917t60","country_code":"MX","type":"education","lineage":["https://openalex.org/I196664497"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Gelasio Salazar","raw_affiliation_strings":["Instituto de F\u0131\u0301sica Universidad Aut\u00f3noma de San Luis Potos\u0131\u0301  San Luis Potosi Mexico"],"affiliations":[{"raw_affiliation_string":"Instituto de F\u0131\u0301sica Universidad Aut\u00f3noma de San Luis Potos\u0131\u0301  San Luis Potosi Mexico","institution_ids":["https://openalex.org/I196664497"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002067531","display_name":"Matthew Sullivan","orcid":"https://orcid.org/0000-0003-4263-0273"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Matthew Sullivan","raw_affiliation_strings":["Department of Combinatorics and Optimization University of Waterloo  Waterloo Ontario Canada","Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization University of Waterloo  Waterloo Ontario Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5060540226"],"corresponding_institution_ids":["https://openalex.org/I196664497"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00991304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"97","issue":"3","first_page":"426","last_page":"440"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9146999716758728,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9146999716758728,"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/T13267","display_name":"Advanced Theoretical and Applied Studies in Material Sciences and Geometry","score":0.902899980545044,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/projective-test","display_name":"Projective test","score":0.6703349947929382},{"id":"https://openalex.org/keywords/projective-plane","display_name":"Projective plane","score":0.661634087562561},{"id":"https://openalex.org/keywords/real-projective-plane","display_name":"Real projective plane","score":0.5098928213119507},{"id":"https://openalex.org/keywords/pencil","display_name":"Pencil (optics)","score":0.4881356656551361},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46852797269821167},{"id":"https://openalex.org/keywords/blocking-set","display_name":"Blocking set","score":0.46640291810035706},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.46555429697036743},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43472516536712646},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.34629151225090027},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.3242379426956177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3202514052391052},{"id":"https://openalex.org/keywords/projective-space","display_name":"Projective space","score":0.2535107135772705},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23404660820960999},{"id":"https://openalex.org/keywords/collineation","display_name":"Collineation","score":0.1577695608139038},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15549024939537048},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.07307809591293335}],"concepts":[{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.6703349947929382},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.661634087562561},{"id":"https://openalex.org/C37470923","wikidata":"https://www.wikidata.org/wiki/Q633815","display_name":"Real projective plane","level":5,"score":0.5098928213119507},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.4881356656551361},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46852797269821167},{"id":"https://openalex.org/C56952292","wikidata":"https://www.wikidata.org/wiki/Q17005980","display_name":"Blocking set","level":5,"score":0.46640291810035706},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.46555429697036743},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43472516536712646},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34629151225090027},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.3242379426956177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3202514052391052},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.2535107135772705},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23404660820960999},{"id":"https://openalex.org/C163434512","wikidata":"https://www.wikidata.org/wiki/Q390741","display_name":"Collineation","level":4,"score":0.1577695608139038},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15549024939537048},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.07307809591293335},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/jgt.22665","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.22665","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.02287","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.02287","pdf_url":"https://arxiv.org/pdf/2002.02287","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2002.02287","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.02287","pdf_url":"https://arxiv.org/pdf/2002.02287","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4627710073","display_name":null,"funder_award_id":"50503\u201010940\u2010500","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W15502516","https://openalex.org/W27506364","https://openalex.org/W1566173313","https://openalex.org/W1952256967","https://openalex.org/W1984830753","https://openalex.org/W2032958186","https://openalex.org/W2056775628","https://openalex.org/W2109042433","https://openalex.org/W2643884685","https://openalex.org/W2805126457","https://openalex.org/W2900334066","https://openalex.org/W4229510153","https://openalex.org/W6676473737","https://openalex.org/W6739719447"],"related_works":["https://openalex.org/W2558849366","https://openalex.org/W2596448680","https://openalex.org/W2585580987","https://openalex.org/W2055709997","https://openalex.org/W2952320063","https://openalex.org/W93742352","https://openalex.org/W2187623611","https://openalex.org/W2013686093","https://openalex.org/W1970976233","https://openalex.org/W4254177151"],"abstract_inverted_index":{"Abstract":[0],"Hill's":[1,95],"Conjecture":[2],"states":[3],"that":[4,22,69,109],"the":[5,9,13,16,23,34,49,56,63,70,89,106],"crossing":[6,57],"number":[7,25,58,72],"of":[8,26,52,59,73,83,91,104],"complete":[10],"graph":[11,61],"in":[12,28,32,62,75,105],"plane":[14,81,108],"(equivalently,":[15],"sphere)":[17],"is":[18,43,84],".":[19,53,85,100],"Moon":[20],"proved":[21,68],"expected":[24,71],"crossings":[27,74],"a":[29,60,76],"spherical":[30],"drawing":[31,82],"which":[33],"points":[35],"are":[36],"randomly":[37],"distributed":[38],"and":[39],"joined":[40],"by":[41],"geodesics":[42],"precisely":[44],",":[45],"thus":[46],"matching":[47],"asymptotically":[48],"conjectured":[50],"value":[51],"Let":[54],"denote":[55],"projective":[64,80,107],"plane.":[65],"Recently,":[66],"Elkies":[67,97],"naturally":[77],"defined":[78],"random":[79],"In":[86],"analogy":[87],"with":[88],"relation":[90],"Moon's":[92],"result":[93],"to":[94],"conjecture,":[96],"asked":[98],"if":[99],"We":[101],"construct":[102],"drawings":[103],"disprove":[110],"this.":[111]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}