{"id":"https://openalex.org/W4210253419","doi":"https://doi.org/10.1142/s0218195921500072","title":"On Edge-Length Ratios of Partial 2-Trees","display_name":"On Edge-Length Ratios of Partial 2-Trees","publication_year":2021,"publication_date":"2021-06-01","ids":{"openalex":"https://openalex.org/W4210253419","doi":"https://doi.org/10.1142/s0218195921500072"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195921500072","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195921500072","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015750491","display_name":"V\u00e1clav Bla\u017ej","orcid":null},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"V\u00e1clav Bla\u017ej","raw_affiliation_strings":["Faculty of Information Technology, Czech Technical University in Prague, Th\u00e1kurova 9, Prague 6, 160 00, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Czech Technical University in Prague, Th\u00e1kurova 9, Prague 6, 160 00, Czech Republic","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088167330","display_name":"Ji\u0159\u0131\u0301 Fiala","orcid":"https://orcid.org/0000-0002-8108-567X"},"institutions":[{"id":"https://openalex.org/I21250087","display_name":"Charles University","ror":"https://ror.org/024d6js02","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21250087"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Ji\u0159\u00ed Fiala","raw_affiliation_strings":["Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, Prague 2, 121 16, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, Prague 2, 121 16, Czech Republic","institution_ids":["https://openalex.org/I21250087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008995859","display_name":"Giuseppe Liotta","orcid":"https://orcid.org/0000-0002-2886-9694"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giuseppe Liotta","raw_affiliation_strings":["Dipartimento di Ingegneria, Universit\u00e0 degli Studi di Perugia, Edificio Presidenza, Perugia 06125, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria, Universit\u00e0 degli Studi di Perugia, Edificio Presidenza, Perugia 06125, Italy","institution_ids":["https://openalex.org/I27483092"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015750491"],"corresponding_institution_ids":["https://openalex.org/I44504214"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.24199021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"31","issue":"02n03","first_page":"141","last_page":"162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9871000051498413,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8167791366577148},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8075129985809326},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6002721190452576},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.5892887115478516},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5571740865707397},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.5265496373176575},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5039116740226746},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4977717697620392},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.4474218487739563},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.43245142698287964},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.36511439085006714},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12823349237442017}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8167791366577148},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8075129985809326},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6002721190452576},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.5892887115478516},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5571740865707397},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.5265496373176575},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5039116740226746},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4977717697620392},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4474218487739563},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.43245142698287964},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.36511439085006714},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12823349237442017},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195921500072","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195921500072","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry & Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W634834491","https://openalex.org/W1579049696","https://openalex.org/W1984127148","https://openalex.org/W2070310809","https://openalex.org/W2102664288","https://openalex.org/W2963536983","https://openalex.org/W3135568625","https://openalex.org/W4240930434","https://openalex.org/W4240983959","https://openalex.org/W4252017042"],"related_works":["https://openalex.org/W2953175190","https://openalex.org/W4288318511","https://openalex.org/W2257286100","https://openalex.org/W2099602951","https://openalex.org/W2784344684","https://openalex.org/W2562705109","https://openalex.org/W4283118620","https://openalex.org/W3130072254","https://openalex.org/W3022748053","https://openalex.org/W4287823747"],"abstract_inverted_index":{"The":[0,45],"edge-length":[1,43,47,61,76,129],"ratio":[2,14,32,39,48,77,130],"of":[3,8,18,21,49,68,78],"a":[4,9,50,90,123],"planar":[5,65,124],"straight-line":[6,66,125],"drawing":[7,126],"graph":[10,51],"is":[11,40,55,84,131],"the":[12,16,25,31,38,56,64,75,79],"maximum":[13],"between":[15],"lengths":[17],"any":[19,138],"two":[20],"its":[22],"edges.":[23],"When":[24],"edges":[26],"to":[27,35],"be":[28,36],"considered":[29],"in":[30,63],"are":[33],"required":[34],"adjacent,":[37],"called":[41],"local":[42,128],"ratio.":[44],"(local)":[46,60],"[Formula:":[52,69,80,85,134,141],"see":[53,70,81,86,135,142],"text]":[54,136],"infimum":[57],"over":[58],"all":[59],"ratios":[62],"drawings":[67],"text].":[71,143],"We":[72,115],"prove":[73,117],"that":[74,118],"text]-vertex":[82],"2-trees":[83],"text],":[87],"which":[88],"proves":[89],"conjecture":[91],"by":[92,106],"Lazard":[93],"et":[94],"al.":[95],"[TCS":[96],"770,":[97],"2019,":[98],"pp.":[99,113],"88\u201394]":[100],"and":[101,108],"complements":[102],"an":[103],"upper":[104],"bound":[105],"Borrazzo":[107],"Frati":[109],"[JoCG":[110],"11(1),":[111],"2020,":[112],"137\u2013155].":[114],"also":[116],"every":[119],"partial":[120],"2-tree":[121],"admits":[122],"whose":[127],"at":[132],"most":[133],"for":[137],"arbitrarily":[139],"small":[140]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}