{"id":"https://openalex.org/W3036322218","doi":"https://doi.org/10.1017/s0963548323000135","title":"Universal geometric graphs","display_name":"Universal geometric graphs","publication_year":2023,"publication_date":"2023-05-15","ids":{"openalex":"https://openalex.org/W3036322218","doi":"https://doi.org/10.1017/s0963548323000135","mag":"3036322218"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548323000135","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1017/s0963548323000135","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"http://dx.doi.org/10.1017/s0963548323000135","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025842302","display_name":"Fabrizio Frati","orcid":"https://orcid.org/0000-0001-5987-8713"},"institutions":[{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabrizio Frati","raw_affiliation_strings":["Department of Engineering, Roma Tre University, Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0001-5987-8713","affiliations":[{"raw_affiliation_string":"Department of Engineering, Roma Tre University, Rome, Italy","institution_ids":["https://openalex.org/I119003972"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103088991","display_name":"Michael M. Hoffmann","orcid":"https://orcid.org/0000-0001-5307-7106"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Michael Hoffmann","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0001-5307-7106","affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"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\u00f3th","raw_affiliation_strings":["Department of Mathematics, California State University Northridge, Los Angeles, CA, USA","Department of Computer Science, Tufts University, Medford, MA, USA"],"raw_orcid":"https://orcid.org/0000-0002-8769-3190","affiliations":[{"raw_affiliation_string":"Department of Mathematics, California State University Northridge, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I157638225"]},{"raw_affiliation_string":"Department of Computer Science, Tufts University, Medford, MA, USA","institution_ids":["https://openalex.org/I121934306"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5103088991"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00262861,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"5","first_page":"742","last_page":"761"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9986000061035156,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9842000007629395,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8593841791152954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7024790048599243},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5923578143119812},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4649708569049835},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4298105239868164},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4172123670578003},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.36767327785491943}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8593841791152954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7024790048599243},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5923578143119812},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4649708569049835},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4298105239868164},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4172123670578003},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36767327785491943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548323000135","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1017/s0963548323000135","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:research-collection.ethz.ch:20.500.11850/619518","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/619518","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability & Computing, 32 (5)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma3.it:11590/465067","is_oa":true,"landing_page_url":"https://hdl.handle.net/11590/465067","pdf_url":"https://iris.uniroma3.it/bitstream/11590/465067/1/PUBLISHED.pdf","source":{"id":"https://openalex.org/S4377196120","display_name":"Iris (Roma Tre University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119003972","host_organization_name":"Roma Tre University","host_organization_lineage":["https://openalex.org/I119003972"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.3929/ethz-b-000619518","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000619518","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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-journal"}],"best_oa_location":{"id":"doi:10.1017/s0963548323000135","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1017/s0963548323000135","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.5899999737739563}],"awards":[{"id":"https://openalex.org/G1727795598","display_name":null,"funder_award_id":"SNSF Project 200021E-171681","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G2878586969","display_name":"RUI: Geometric Intersection Graphs","funder_award_id":"1800734","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4194657088","display_name":"Arrangements and Drawings (ArrDra)","funder_award_id":"171681","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4744268795","display_name":null,"funder_award_id":"PRIN 20174LF3T8","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G5143266877","display_name":null,"funder_award_id":"20174LF3T8","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G6547511553","display_name":null,"funder_award_id":"20174LF3T8","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8158069009","display_name":null,"funder_award_id":"200021E-171681","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W999599142","https://openalex.org/W1573857958","https://openalex.org/W1605337124","https://openalex.org/W1906724808","https://openalex.org/W1978917076","https://openalex.org/W1991646384","https://openalex.org/W1994115477","https://openalex.org/W1996196886","https://openalex.org/W1997180465","https://openalex.org/W1997949020","https://openalex.org/W1998294201","https://openalex.org/W2003525146","https://openalex.org/W2005387480","https://openalex.org/W2049284557","https://openalex.org/W2052690504","https://openalex.org/W2076787978","https://openalex.org/W2087086535","https://openalex.org/W2090891537","https://openalex.org/W2091514779","https://openalex.org/W2100223096","https://openalex.org/W2131867452","https://openalex.org/W2478461887","https://openalex.org/W2531046989","https://openalex.org/W2567966754","https://openalex.org/W2571485474","https://openalex.org/W2807135142","https://openalex.org/W2950472592","https://openalex.org/W3001673916","https://openalex.org/W3009498706","https://openalex.org/W3019053352","https://openalex.org/W3100879432","https://openalex.org/W3101229799","https://openalex.org/W3105608782","https://openalex.org/W3204812806","https://openalex.org/W4211173638","https://openalex.org/W4237169760","https://openalex.org/W4285707433","https://openalex.org/W6626141462"],"related_works":["https://openalex.org/W4360764540","https://openalex.org/W2963028755","https://openalex.org/W4231657010","https://openalex.org/W2395986200","https://openalex.org/W1994552539","https://openalex.org/W2007917622","https://openalex.org/W1606013690","https://openalex.org/W4293743430","https://openalex.org/W3006156235","https://openalex.org/W2073591271"],"abstract_inverted_index":{"Abstract":[0],"We":[1,120],"extend":[2],"the":[3,157,164],"notion":[4],"of":[5,22,35,104,142],"universal":[6,16,62,132,193],"graphs":[7,24,137],"to":[8],"a":[9,18,32,49,69,99,139],"geometric":[10,13,50,128,169,181],"setting.":[11],"A":[12],"graph":[14,37,51,83,129,182],"is":[15,45,61,131,192],"for":[17,63,133,148,194],"class":[19],"$\\mathcal":[20,39],"H$":[21,40],"planar":[23],"if":[25,113],"it":[26],"contains":[27,93],"an":[28,81,177],"embedding,":[29],"that":[30,46,60,78,92,123,130,174,191],"is,":[31],"crossing-free":[33],"drawing,":[34],"every":[36,94,124,149],"in":[38],".":[41],"Our":[42],"main":[43],"result":[44,71],"there":[47,79,175],"exists":[48,80,176],"with":[52,84,183],"$n$":[53,64,85,95,116,125,134,165,178,184,195],"vertices":[54,86,117,185],"and":[55,74,87,186],"$O\\!\\left(n":[56,88,105,187],"\\log":[57,89,106,188],"n\\right)$":[58,90,107,189],"edges":[59,91,108,190],"-vertex":[65,96,126,135,166,179,196],"forests;":[66],"this":[67,154],"generalises":[68],"well-known":[70],"by":[72,163],"Chung":[73],"Graham,":[75],"which":[76],"states":[77],"(abstract)":[82],"forest":[97],"as":[98],"subgraph.":[100],"The":[101],"upper":[102,160],"bound":[103,161],"cannot":[109],"be":[110],"improved,":[111],"even":[112],"more":[114],"than":[115],"are":[118],"allowed.":[119],"also":[121],"prove":[122,173],"convex":[127,168,180],"outerplanar":[136],"has":[138],"near-quadratic":[140],"number":[141],"edges,":[143],"namely":[144],"$\\Omega":[145],"_h(n^{2-1/h})$":[146],",":[147],"positive":[150],"integer":[151],"$h$":[152],";":[153],"almost":[155],"matches":[156],"trivial":[158],"$O(n^2)$":[159],"given":[162],"complete":[167],"graph.":[170],"Finally,":[171],"we":[172],"caterpillars.":[197]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}
