{"id":"https://openalex.org/W1763604081","doi":"https://doi.org/10.37236/10521","title":"The Density of Fan-Planar Graphs","display_name":"The Density of Fan-Planar Graphs","publication_year":2022,"publication_date":"2022-02-11","ids":{"openalex":"https://openalex.org/W1763604081","doi":"https://doi.org/10.37236/10521","mag":"1763604081"},"language":"en","primary_location":{"id":"doi:10.37236/10521","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10521","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p29/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p29/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103045561","display_name":"Michael Kaufmann","orcid":"https://orcid.org/0000-0001-9186-3538"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michael Kaufmann","raw_affiliation_strings":["Eberhard Karls Universit\\\"at T\\\"ubingen","University of T\u00fcbingen"],"affiliations":[{"raw_affiliation_string":"Eberhard Karls Universit\\\"at T\\\"ubingen","institution_ids":["https://openalex.org/I8087733"]},{"raw_affiliation_string":"University of T\u00fcbingen","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063296115","display_name":"Torsten Ueckerdt","orcid":"https://orcid.org/0000-0002-0645-9715"},"institutions":[{"id":"https://openalex.org/I102335020","display_name":"Karlsruhe Institute of Technology","ror":"https://ror.org/04t3en479","country_code":"DE","type":"education","lineage":["https://openalex.org/I102335020","https://openalex.org/I1305996414"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Torsten Ueckerdt","raw_affiliation_strings":["Karlsruhe Institute of Technology","Karlsruhe Institute of technology"],"affiliations":[{"raw_affiliation_string":"Karlsruhe Institute of Technology","institution_ids":["https://openalex.org/I102335020"]},{"raw_affiliation_string":"Karlsruhe Institute of technology","institution_ids":["https://openalex.org/I102335020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103045561"],"corresponding_institution_ids":["https://openalex.org/I8087733"],"apc_list":null,"apc_paid":null,"fwci":1.4545,"has_fulltext":true,"cited_by_count":44,"citation_normalized_percentile":{"value":0.85948905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"1","first_page":null,"last_page":null},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9883999824523926,"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"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9765999913215637,"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":0.7528358101844788},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7345067262649536},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6443719863891602},{"id":"https://openalex.org/keywords/outerplanar-graph","display_name":"Outerplanar graph","score":0.5233228206634521},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.46236637234687805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4541352391242981},{"id":"https://openalex.org/keywords/topological-graph","display_name":"Topological graph","score":0.44283297657966614},{"id":"https://openalex.org/keywords/multiple-edges","display_name":"Multiple edges","score":0.4378368854522705},{"id":"https://openalex.org/keywords/book-embedding","display_name":"Book embedding","score":0.42043575644493103},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40288046002388},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.3962864875793457},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.29865795373916626}],"concepts":[{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.7528358101844788},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7345067262649536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6443719863891602},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.5233228206634521},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.46236637234687805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4541352391242981},{"id":"https://openalex.org/C8764922","wikidata":"https://www.wikidata.org/wiki/Q17104195","display_name":"Topological graph","level":3,"score":0.44283297657966614},{"id":"https://openalex.org/C103257674","wikidata":"https://www.wikidata.org/wiki/Q6934937","display_name":"Multiple edges","level":3,"score":0.4378368854522705},{"id":"https://openalex.org/C180222743","wikidata":"https://www.wikidata.org/wiki/Q4942980","display_name":"Book embedding","level":5,"score":0.42043575644493103},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40288046002388},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3962864875793457},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.29865795373916626}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/10521","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10521","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p29/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1403.6184","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1403.6184","pdf_url":"https://arxiv.org/pdf/1403.6184","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":"text"},{"id":"mag:1763604081","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1403.6184.pdf","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.1403.6184","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1403.6184","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:10.37236/10521","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10521","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p29/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/W1763604081.pdf","grobid_xml":"https://content.openalex.org/works/W1763604081.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W42881399","https://openalex.org/W49135760","https://openalex.org/W158349004","https://openalex.org/W165147621","https://openalex.org/W185123065","https://openalex.org/W1479684016","https://openalex.org/W1539895965","https://openalex.org/W1582137572","https://openalex.org/W1594340659","https://openalex.org/W1648748816","https://openalex.org/W1723997437","https://openalex.org/W1879570458","https://openalex.org/W1903431984","https://openalex.org/W1959141466","https://openalex.org/W1967421215","https://openalex.org/W1981505946","https://openalex.org/W2003525146","https://openalex.org/W2021281967","https://openalex.org/W2040261757","https://openalex.org/W2047142187","https://openalex.org/W2072233942","https://openalex.org/W2079157536","https://openalex.org/W2082388593","https://openalex.org/W2083421046","https://openalex.org/W2087120634","https://openalex.org/W2091733471","https://openalex.org/W2091855373","https://openalex.org/W2122778940","https://openalex.org/W2134344894","https://openalex.org/W2143831227","https://openalex.org/W2149247378","https://openalex.org/W2149954650","https://openalex.org/W2151056011","https://openalex.org/W2204635654","https://openalex.org/W2247922300","https://openalex.org/W2275362914","https://openalex.org/W2295628431","https://openalex.org/W2487036166","https://openalex.org/W2500153981","https://openalex.org/W2615925897","https://openalex.org/W2775046532","https://openalex.org/W2796841069","https://openalex.org/W2898765768","https://openalex.org/W2899777575","https://openalex.org/W2963804516","https://openalex.org/W2965781953","https://openalex.org/W3196892319"],"related_works":["https://openalex.org/W1723997437","https://openalex.org/W1594340659","https://openalex.org/W2775046532","https://openalex.org/W1967421215","https://openalex.org/W2151056011","https://openalex.org/W2072233942","https://openalex.org/W2570781789","https://openalex.org/W2122778940","https://openalex.org/W2083421046","https://openalex.org/W2899777575","https://openalex.org/W2047142187","https://openalex.org/W2799803339","https://openalex.org/W1479684016","https://openalex.org/W3123018062","https://openalex.org/W2248326503","https://openalex.org/W2159869336","https://openalex.org/W192589467","https://openalex.org/W3104418588","https://openalex.org/W1993083969","https://openalex.org/W1990163141"],"abstract_inverted_index":{"A":[0,33,87],"topological":[1,88,114,255],"drawing":[2,89,182,207],"of":[3,23,53,85,113,149,172,180,213,254,266,304],"a":[4,18,37,41,79,106,169,205,210,281],"graph":[5,35,38,155,161,181,194,295],"is":[6,25,36,55,60,72,90,156,162,218,271],"fan-planar":[7,34,134,157,160,193,206,228,246,278],"if":[8,92],"for":[9,220,261,289],"each":[10],"edge":[11],"$e$":[12,16,24,28,59,71],"the":[13,56,67,110,178,232,263],"edges":[14,65,77,95,267],"crossing":[15,31],"form":[17,248],"star":[19],"and":[20,29,66,125,129,158,183,239,302],"no":[21],"endpoint":[22,84],"enclosed":[26],"by":[27,48,62,74,117,258],"its":[30],"edges.":[32],"admitting":[39],"such":[40,121],"drawing.":[42,296],"Equivalently,":[43],"this":[44,187,286],"can":[45],"be":[46],"formulated":[47],"three":[49],"forbidden":[50,118,259],"patterns,":[51,120,260],"one":[52,99],"which":[54,217,262,284],"configuration":[57],"where":[58,70],"crossed":[61,73],"two":[63,69,75,94],"independent":[64],"other":[68],"incident":[76],"in":[78,101,109,141,146,168,231,294],"way":[80],"that":[81,191,276],"encloses":[82],"some":[83],"$e$.":[86],"simple":[91],"any":[93],"have":[96,209],"at":[97,199],"most":[98,200],"point":[100],"common.":[102],"Fan-planar":[103],"graphs":[104,115,124,135,176,229,236,241,247,256,279],"are":[105],"new":[107,306],"member":[108],"ever-growing":[111],"list":[112],"defined":[116,257],"intersection":[119],"as":[122],"planar":[123,235],"their":[126],"generalizations,":[127],"Tur\u00e1n-graphs":[128],"Conway's":[130],"thrackle":[131],"conjecture.":[132],"Hence":[133],"fall":[136],"into":[137],"an":[138,249],"important":[139],"field":[140],"combinatorial":[142,184],"geometry":[143],"with":[144,234],"applications":[145],"various":[147],"areas":[148,179],"discrete":[150],"mathematics.":[151],"As":[152],"every":[153,159,192,221],"$1$-planar":[154,240],"$3$-quasiplanar,":[163],"they":[164],"also":[165],"fit":[166,230],"perfectly":[167],"recent":[170],"series":[171],"works":[173],"on":[174,195,268],"nearly-planar":[175],"from":[177],"embeddings.":[185],"In":[186],"paper":[188],"we":[189,298],"show":[190],"$n$":[196,269],"vertices":[197,270],"has":[198],"$5n-10$":[201],"edges,":[202],"even":[203],"though":[204],"may":[208],"quadratic":[211],"number":[212,265],"crossings.":[214],"Our":[215],"bound,":[216],"tight":[219],"$n":[222],"\\geq":[223],"20$,":[224],"indicates":[225],"how":[226],"nicely":[227],"row":[233],"($3n-6$":[237],"edges)":[238],"($4n-8$":[242],"edges).":[243],"With":[244],"this,":[245],"inclusion-wise":[250],"largest":[251],"non-trivial":[252],"class":[253,287],"maximum":[264,277],"known":[272],"exactly.":[273],"We":[274],"demonstrate":[275],"carry":[280],"rich":[282],"structure,":[283],"makes":[285],"attractive":[288],"many":[290],"algorithms":[291],"commonly":[292],"used":[293],"Finally,":[297],"discuss":[299],"possible":[300],"extensions":[301],"generalizations":[303],"these":[305],"concepts.":[307]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
