{"id":"https://openalex.org/W2949607879","doi":"https://doi.org/10.1017/s0963548317000141","title":"Convex Polygons in Geometric Triangulations","display_name":"Convex Polygons in Geometric Triangulations","publication_year":2017,"publication_date":"2017-05-30","ids":{"openalex":"https://openalex.org/W2949607879","doi":"https://doi.org/10.1017/s0963548317000141","mag":"2949607879"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548317000141","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548317000141","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1411.1303","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091313409","display_name":"Adrian Dumitrescu","orcid":"https://orcid.org/0000-0002-1118-0321"},"institutions":[{"id":"https://openalex.org/I43579087","display_name":"University of Wisconsin\u2013Milwaukee","ror":"https://ror.org/031q21x57","country_code":"US","type":"education","lineage":["https://openalex.org/I43579087"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"ADRIAN DUMITRESCU","raw_affiliation_strings":["Department of Computer Science, University of Wisconsin\u2013Milwaukee, USA (e-mail:","Department of Computer Science, University of Wisconsin-Milwaukee, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Wisconsin\u2013Milwaukee, USA (e-mail:","institution_ids":["https://openalex.org/I43579087"]},{"raw_affiliation_string":"Department of Computer Science, University of Wisconsin-Milwaukee, USA","institution_ids":["https://openalex.org/I43579087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030799674","display_name":"Csaba D. T\u00f3th","orcid":"https://orcid.org/0000-0002-8769-3190"},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]},{"id":"https://openalex.org/I157638225","display_name":"California State University, Northridge","ror":"https://ror.org/005f5hv41","country_code":"US","type":"education","lineage":["https://openalex.org/I157638225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"CSABA D. T\u00d3TH","raw_affiliation_strings":["Department of Computer Science, Tufts University, Medford, MA, USA (e-mail:","Department of Mathematics, California State University Northridge, Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Tufts University, Medford, MA, USA (e-mail:","institution_ids":["https://openalex.org/I121934306"]},{"raw_affiliation_string":"Department of Mathematics, California State University Northridge, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I157638225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1705,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.89343517,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"5","first_page":"641","last_page":"659"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"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":1.0,"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":0.9958000183105469,"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/T10191","display_name":"Robotics and Sensor-Based Localization","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/combinatorics","display_name":"Combinatorics","score":0.7923067808151245},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.7763867378234863},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5778666734695435},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.5578935146331787},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5421872735023499},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.5057809352874756},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.503656804561615},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4632294178009033},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4249875247478485},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.38796383142471313},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3674558103084564},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16990387439727783},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12736156582832336},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12514635920524597}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7923067808151245},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.7763867378234863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5778666734695435},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.5578935146331787},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5421872735023499},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.5057809352874756},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.503656804561615},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4632294178009033},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4249875247478485},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38796383142471313},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3674558103084564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16990387439727783},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12736156582832336},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12514635920524597},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548317000141","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548317000141","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1411.1303","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.1303","pdf_url":"https://arxiv.org/pdf/1411.1303","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:1411.1303","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.1303","pdf_url":"https://arxiv.org/pdf/1411.1303","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W13988344","https://openalex.org/W67063475","https://openalex.org/W1487872891","https://openalex.org/W1965976352","https://openalex.org/W1994969571","https://openalex.org/W2000008376","https://openalex.org/W2004367845","https://openalex.org/W2028071467","https://openalex.org/W2055728458","https://openalex.org/W2062138633","https://openalex.org/W2069367490","https://openalex.org/W2083028555","https://openalex.org/W2085179971","https://openalex.org/W2090290344","https://openalex.org/W2096398399","https://openalex.org/W2102047759","https://openalex.org/W2110861431","https://openalex.org/W2120554500","https://openalex.org/W2129047612","https://openalex.org/W2161968825","https://openalex.org/W2163448076","https://openalex.org/W2172269549","https://openalex.org/W2303808417","https://openalex.org/W2503695081","https://openalex.org/W2507818253","https://openalex.org/W2569928643","https://openalex.org/W2914876106","https://openalex.org/W2949607879","https://openalex.org/W2951901759","https://openalex.org/W2952558346","https://openalex.org/W2952626446","https://openalex.org/W3105284723","https://openalex.org/W4243262670","https://openalex.org/W4246219036","https://openalex.org/W4247988438","https://openalex.org/W4300809055","https://openalex.org/W6600579306"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W2281248943","https://openalex.org/W3102538728","https://openalex.org/W2073023540"],"abstract_inverted_index":{"We":[0],"show":[1,69],"that":[2],"the":[3,16,44,55,74],"maximum":[4],"number":[5,75],"of":[6,12,28,49,76],"convex":[7,77],"polygons":[8,78],"in":[9,15,79],"a":[10,59],"triangulation":[11],"n":[13,21,31,51,65],"points":[14],"plane":[17],"is":[18],"O":[19,29],"(1.5029":[20],").":[22],"This":[23],"improves":[24],"an":[25],"earlier":[26],"bound":[27,48],"(1.6181":[30],")":[32,52],"established":[33],"by":[34],"van":[35],"Kreveld,":[36],"L\u00f6ffler":[37],"and":[38,41],"Pach":[39],"(2012),":[40],"almost":[42],"matches":[43],"current":[45],"best":[46],"lower":[47],"\u03a9(1.5028":[50],"due":[53],"to":[54,71],"same":[56],"authors.":[57],"Given":[58],"planar":[60],"straight-line":[61],"graph":[62],"G":[63,80],"with":[64],"vertices,":[66],"we":[67],"also":[68],"how":[70],"compute":[72],"efficiently":[73],".":[81]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}