{"id":"https://openalex.org/W2150037097","doi":"https://doi.org/10.1007/s00373-010-0957-2","title":"Every Large Point Set contains Many Collinear Points or an Empty Pentagon","display_name":"Every Large Point Set contains Many Collinear Points or an Empty Pentagon","publication_year":2010,"publication_date":"2010-10-06","ids":{"openalex":"https://openalex.org/W2150037097","doi":"https://doi.org/10.1007/s00373-010-0957-2","mag":"2150037097"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-010-0957-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-010-0957-2","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0904.0262","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zachary Abel","orcid":null},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zachary Abel","raw_affiliation_strings":["Department of Mathematics, Harvard University, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harvard University, Cambridge, MA, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Brad Ballinger","orcid":null},"institutions":[{"id":"https://openalex.org/I192389796","display_name":"Humboldt State University","ror":"https://ror.org/02qt0xs84","country_code":"US","type":"education","lineage":["https://openalex.org/I192389796"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brad Ballinger","raw_affiliation_strings":["Department of Mathematics, Humboldt State University, California, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Humboldt State University, California, USA","institution_ids":["https://openalex.org/I192389796"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Prosenjit Bose","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Prosenjit Bose","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":null,"display_name":"S\u00e9bastien Collette","orcid":null},"institutions":[{"id":"https://openalex.org/I17653759","display_name":"Fund for Scientific Research","ror":"https://ror.org/03q83t159","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I17653759"]},{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"S\u00e9bastien Collette","raw_affiliation_strings":["Charg\u00e9 de Recherches du F.R.S.-FNRS, D\u00e9partement d\u2019Informatique, Universit\u00e9 Libre de Bruxelles, Brussels, Belgium"],"affiliations":[{"raw_affiliation_string":"Charg\u00e9 de Recherches du F.R.S.-FNRS, D\u00e9partement d\u2019Informatique, Universit\u00e9 Libre de Bruxelles, Brussels, Belgium","institution_ids":["https://openalex.org/I132053463","https://openalex.org/I17653759"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Vida Dujmovi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vida Dujmovi\u0107","raw_affiliation_strings":["School of Computer Science, Carleton University, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carleton University, Ottawa, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ferran Hurtado","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ferran Hurtado","raw_affiliation_strings":["Departament de Matem\u00e0tica Aplicada II, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada II, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Scott Duke Kominers","orcid":null},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott Duke Kominers","raw_affiliation_strings":["Department of Economics, Harvard University, and Harvard Business School, Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Economics, Harvard University, and Harvard Business School, Boston, MA, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Stefan Langerman","orcid":null},"institutions":[{"id":"https://openalex.org/I17653759","display_name":"Fund for Scientific Research","ror":"https://ror.org/03q83t159","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I17653759"]},{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Stefan Langerman","raw_affiliation_strings":["Ma\u00eetre de Recherches du F.R.S.-FNRS, D\u00e9partement d\u2019Informatique, Universit\u00e9 Libre de Bruxelles, Brussels, Belgium"],"affiliations":[{"raw_affiliation_string":"Ma\u00eetre de Recherches du F.R.S.-FNRS, D\u00e9partement d\u2019Informatique, Universit\u00e9 Libre de Bruxelles, Brussels, Belgium","institution_ids":["https://openalex.org/I132053463","https://openalex.org/I17653759"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Attila P\u00f3r","orcid":null},"institutions":[{"id":"https://openalex.org/I94339441","display_name":"Western Kentucky University","ror":"https://ror.org/0446vnd56","country_code":"US","type":"education","lineage":["https://openalex.org/I94339441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Attila P\u00f3r","raw_affiliation_strings":["Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky, USA","institution_ids":["https://openalex.org/I94339441"]}]},{"author_position":"last","author":{"id":null,"display_name":"David R. Wood","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"David R. Wood","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Melbourne, Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":10,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.3257,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.93507025,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"27","issue":"1","first_page":"47","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.6966000199317932,"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":0.6966000199317932,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.10409999638795853,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.07810000330209732,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/pentagon","display_name":"Pentagon","score":0.8914999961853027},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6879000067710876},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6394000053405762},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5453000068664551},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5062000155448914},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4964999854564667}],"concepts":[{"id":"https://openalex.org/C2779965921","wikidata":"https://www.wikidata.org/wiki/Q127840","display_name":"Pentagon","level":2,"score":0.8914999961853027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8414000272750854},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.785099983215332},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6879000067710876},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6394000053405762},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5453000068664551},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5062000155448914},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4964999854564667},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4260999858379364},{"id":"https://openalex.org/C182124507","wikidata":"https://www.wikidata.org/wiki/Q166154","display_name":"Line segment","level":2,"score":0.301800012588501},{"id":"https://openalex.org/C2779511736","wikidata":"https://www.wikidata.org/wiki/Q2983383","display_name":"Necklace","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C170320093","wikidata":"https://www.wikidata.org/wiki/Q1953457","display_name":"De Bruijn sequence","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2556999921798706}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00373-010-0957-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00373-010-0957-2","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0904.0262","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0904.0262","pdf_url":"https://arxiv.org/pdf/0904.0262","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"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/71138","is_oa":false,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/71138","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Graphs and combinatorics, 27 (1","raw_type":"info:ulb-repo/semantics/openurl/article"},{"id":"pmh:oai:upcommons.upc.edu:2117/11669","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/11669","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0904.0262","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0904.0262","pdf_url":"https://arxiv.org/pdf/0904.0262","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1486040170","https://openalex.org/W1488784459","https://openalex.org/W1493472025","https://openalex.org/W1789265278","https://openalex.org/W1967761664","https://openalex.org/W1970934335","https://openalex.org/W1977266879","https://openalex.org/W1987886060","https://openalex.org/W2006073641","https://openalex.org/W2014439009","https://openalex.org/W2018024429","https://openalex.org/W2028119184","https://openalex.org/W2029537887","https://openalex.org/W2044868365","https://openalex.org/W2071851628","https://openalex.org/W2072495759","https://openalex.org/W2072795940","https://openalex.org/W2072869041","https://openalex.org/W2083028555","https://openalex.org/W2087585583","https://openalex.org/W2090067893","https://openalex.org/W2107711450","https://openalex.org/W2134189835","https://openalex.org/W2153441850","https://openalex.org/W2157290820","https://openalex.org/W2167816765","https://openalex.org/W2170459217","https://openalex.org/W4242510827","https://openalex.org/W4248701726"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2016-06-24T00:00:00"}