{"id":"https://openalex.org/W2901475070","doi":"https://doi.org/10.1007/978-3-030-35802-0_27","title":"A Note on Universal Point Sets for Planar Graphs","display_name":"A Note on Universal Point Sets for Planar Graphs","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2901475070","doi":"https://doi.org/10.1007/978-3-030-35802-0_27","mag":"2901475070"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-35802-0_27","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-35802-0_27","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.7155/jgaa.00529","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078050536","display_name":"Manfred Scheucher","orcid":"https://orcid.org/0000-0002-1657-9796"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Manfred Scheucher","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany","Technical University of Berlin"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Technical University of Berlin","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084244647","display_name":"Hendrik Schrezenmaier","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hendrik Schrezenmaier","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany","Technical University of Berlin"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Technical University of Berlin","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048260458","display_name":"Raphael Steiner","orcid":"https://orcid.org/0000-0002-4234-6136"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Raphael Steiner","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany","Technical University of Berlin"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Technical University of Berlin","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078050536"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.60227273,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68052564,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"24","issue":"3","first_page":"247","last_page":"267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T11164","display_name":"Remote Sensing and LiDAR Applications","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/planar-graph","display_name":"Planar graph","score":0.8233532309532166},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7303210496902466},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.7176874876022339},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5965972542762756},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5957188010215759},{"id":"https://openalex.org/keywords/planar-straight-line-graph","display_name":"Planar straight-line graph","score":0.46682116389274597},{"id":"https://openalex.org/keywords/book-embedding","display_name":"Book embedding","score":0.44888463616371155},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.42648112773895264},{"id":"https://openalex.org/keywords/outerplanar-graph","display_name":"Outerplanar graph","score":0.4230848550796509},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.4208720028400421},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.3980088233947754},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3799333870410919},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.34517210721969604},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.2622706890106201},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21428844332695007},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19166845083236694},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16597729921340942}],"concepts":[{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.8233532309532166},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7303210496902466},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.7176874876022339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5965972542762756},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5957188010215759},{"id":"https://openalex.org/C131930043","wikidata":"https://www.wikidata.org/wiki/Q7200964","display_name":"Planar straight-line graph","level":5,"score":0.46682116389274597},{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.44888463616371155},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42648112773895264},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.4230848550796509},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.4208720028400421},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.3980088233947754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3799333870410919},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.34517210721969604},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.2622706890106201},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21428844332695007},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19166845083236694},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16597729921340942},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/978-3-030-35802-0_27","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-35802-0_27","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"doi:10.7155/jgaa.00529","is_oa":true,"landing_page_url":"https://doi.org/10.7155/jgaa.00529","pdf_url":null,"source":{"id":"https://openalex.org/S33451491","display_name":"Journal of Graph Algorithms and Applications","issn_l":"1526-1719","issn":["1526-1719"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Algorithms and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1811.06482","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.06482","pdf_url":"https://arxiv.org/pdf/1811.06482","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":"","raw_type":null},{"id":"mag:2901475070","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1811.06482","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1811.06482","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1811.06482","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.7155/jgaa.00529","is_oa":true,"landing_page_url":"https://doi.org/10.7155/jgaa.00529","pdf_url":null,"source":{"id":"https://openalex.org/S33451491","display_name":"Journal of Graph Algorithms and Applications","issn_l":"1526-1719","issn":["1526-1719"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Algorithms and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W16939786","https://openalex.org/W202496218","https://openalex.org/W1518705996","https://openalex.org/W1573857958","https://openalex.org/W1807469705","https://openalex.org/W1980218144","https://openalex.org/W1981505946","https://openalex.org/W1990600049","https://openalex.org/W1999600491","https://openalex.org/W2003525146","https://openalex.org/W2029095819","https://openalex.org/W2031515286","https://openalex.org/W2076787978","https://openalex.org/W2079723511","https://openalex.org/W2090891537","https://openalex.org/W2091514779","https://openalex.org/W2099755197","https://openalex.org/W2122264000","https://openalex.org/W2205343714","https://openalex.org/W2571485474","https://openalex.org/W2807135142","https://openalex.org/W2911399207","https://openalex.org/W2969958226","https://openalex.org/W2991434353","https://openalex.org/W3021446987","https://openalex.org/W3135276287"],"related_works":["https://openalex.org/W3019053352","https://openalex.org/W2964163609","https://openalex.org/W2910123141","https://openalex.org/W2058678665","https://openalex.org/W1563721641","https://openalex.org/W2963407690","https://openalex.org/W2119795420","https://openalex.org/W2149888405","https://openalex.org/W3002061974","https://openalex.org/W2949542618","https://openalex.org/W2248326503","https://openalex.org/W2604341771","https://openalex.org/W1857247017","https://openalex.org/W2246774873","https://openalex.org/W2011729204","https://openalex.org/W3134973793","https://openalex.org/W1577386848","https://openalex.org/W2099520181","https://openalex.org/W1763604081","https://openalex.org/W2339884579"],"abstract_inverted_index":{"We":[0,20,67,131],"investigate":[1],"which":[2,77,138],"planar":[3,12,38,79,100,135,165],"point":[4],"sets":[5,114,123],"allow":[6],"simultaneous":[7],"straight-line":[8,33],"embeddings":[9],"of":[10,18,35,72,115,124,146,159],"all":[11,78,99],"graphs":[13,81,101,137,166],"on":[14,63,76,102,111,143],"a":[15,32,156,172],"fixed":[16],"number":[17],"vertices.":[19],"first":[21],"show":[22,68],"that":[23,69,98],"at":[24],"least":[25],"$(1.293-o(1))n$":[26],"points":[27,74,117],"are":[28,41,120],"required":[29],"to":[30],"find":[31],"drawing":[34],"each":[36],"$n$-vertex":[37],"graph":[39],"(vertices":[40],"drawn":[42,85,110,142,169],"as":[43],"the":[44,49,90,160],"given":[45],"points);":[46],"this":[47],"improves":[48],"previous":[50],"best":[51],"constant":[52],"$1.235$":[53],"by":[54,92,175],"Kurowski":[55],"(2004).":[56],"Our":[57],"second":[58],"main":[59],"result":[60,91],"is":[61,152],"based":[62],"exhaustive":[64],"computer":[65],"search:":[66],"no":[70,121],"set":[71,145],"11":[73,147],"exists,":[75],"11-vertex":[80,136],"can":[82,107,167],"be":[83,108,140,168],"simultaneously":[84,109,141,170],"plane":[86],"straight-line.":[87],"This":[88],"strengthens":[89],"Cardinal,":[93],"Hoffmann,":[94],"and":[95,184],"Kusters":[96],"(2015),":[97],"$n":[103,128],"\\le":[104],"10$":[105],"vertices":[106],"particular":[112],"$n$-universal":[113,122],"$n$":[116,126],"while":[118],"there":[119],"size":[125],"for":[127],"\\ge":[129],"15$.":[130],"also":[132],"provide":[133],"49":[134],"cannot":[139],"any":[144],"points.":[148],"This,":[149],"in":[150],"fact,":[151],"another":[153],"step":[154],"towards":[155],"(negative)":[157],"answer":[158],"question,":[161],"whether":[162],"every":[163],"two":[164],"-":[171],"question":[173],"raised":[174],"Brass,":[176],"Cenek,":[177],"Duncan,":[178],"Efrat,":[179],"Erten,":[180],"Ismailescu,":[181],"Kobourov,":[182],"Lubiw,":[183],"Mitchell":[185],"(2007).":[186]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}