{"id":"https://openalex.org/W7223142186","doi":"https://doi.org/10.48550/arxiv.2610.28030","title":"Logarithmic edge-length ratios for planar drawings of 2-trees","display_name":"Logarithmic edge-length ratios for planar drawings of 2-trees","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223142186","doi":"https://doi.org/10.48550/arxiv.2610.28030"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28030","pdf_url":"https://arxiv.org/pdf/2610.28030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.28030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159184777","display_name":"Zahra Sabaei","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sabaei, Zahra","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073258124","display_name":"Fatemeh Emami","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Emami, Fatemeh","raw_affiliation_strings":["Amirkabir University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amirkabir University of Technology","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114336486","display_name":"Yasmin Tousinejad","orcid":"https://orcid.org/0000-0002-6860-9985","observed_orcids":["https://orcid.org/0000-0002-6860-9985"]},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Tousinejad, Yasmin","raw_affiliation_strings":["Amirkabir University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amirkabir University of Technology","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.3578999936580658,"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":0.3578999936580658,"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":0.2694999873638153,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.24410000443458557,"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/2-trees","display_name":"2-trees","score":0.8659999966621399},{"id":"https://openalex.org/keywords/planar-straight-line-drawings","display_name":"planar straight-line drawings","score":0.9629999995231628},{"id":"https://openalex.org/keywords/edge-length-ratio","display_name":"edge length ratio","score":0.7630000114440918},{"id":"https://openalex.org/keywords/logarithmic-bounds","display_name":"logarithmic bounds","score":0.800000011920929},{"id":"https://openalex.org/keywords/network-visualization","display_name":"network visualization","score":0.4309999942779541},{"id":"https://openalex.org/keywords/bar-construction","display_name":"bar construction","score":0.574999988079071},{"id":"https://openalex.org/keywords/planar-graphs","display_name":"planar graphs","score":0.6029999852180481}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8258000016212463},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.8084999918937683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7150999903678894},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6941999793052673},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6639999747276306},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5412999987602234},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.49869999289512634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4812999963760376},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.43790000677108765},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4287000000476837},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3479999899864197},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C131930043","wikidata":"https://www.wikidata.org/wiki/Q7200964","display_name":"Planar straight-line graph","level":5,"score":0.31839999556541443},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28030","pdf_url":"https://arxiv.org/pdf/2610.28030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.2610.28030","doi":"https://doi.org/10.48550/arxiv.2610.28030","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28030","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.28030","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28030","pdf_url":"https://arxiv.org/pdf/2610.28030","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223142186.pdf","grobid_xml":"https://content.openalex.org/works/W7223142186.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1981227591","https://openalex.org/W1984127148","https://openalex.org/W2001019475","https://openalex.org/W2093676108","https://openalex.org/W2603174436","https://openalex.org/W2752590370","https://openalex.org/W3082140337","https://openalex.org/W4210253419","https://openalex.org/W7128421218"],"related_works":["https://openalex.org/W3135568625","https://openalex.org/W4210253419","https://openalex.org/W3082140337","https://openalex.org/W2967793361","https://openalex.org/W2752590370","https://openalex.org/W4408961034","https://openalex.org/W4389073393","https://openalex.org/W2412130227","https://openalex.org/W7098745176","https://openalex.org/W1876331490"],"abstract_inverted_index":{"For":[0],"a":[1,85],"planar":[2,28],"graph":[3],"$G$":[4,39],"with":[5,52],"at":[6],"least":[7],"one":[8],"edge,":[9],"let":[10],"$\u03c1(G)$":[11,66],"be":[12],"the":[13,16,19,22,44,53,63],"infimum":[14],"of":[15,18,31,56,65],"ratio":[17],"longest":[20],"to":[21],"shortest":[23],"edge":[24],"length":[25],"over":[26,67],"all":[27],"straight-line":[29],"drawings":[30],"$G$.":[32],"We":[33],"prove":[34],"that":[35,62],"every":[36],"$n$-vertex":[37,68],"$2$-tree":[38],"satisfies":[40],"$\u03c1(G)\\le4+5\\lfloor\\log_2(2n-3)\\rfloor$.":[41],"This":[42],"improves":[43],"known":[45],"$O(\\sqrt":[46],"n)$":[47],"upper":[48],"bound":[49,55],"and,":[50],"together":[51],"lower":[54],"Bla\u017eej,":[57],"Fiala":[58],"and":[59,83],"Liotta,":[60],"shows":[61],"maximum":[64],"$2$-trees":[69],"is":[70],"$\u0398(\\log":[71],"n)$.":[72],"The":[73],"proof":[74],"adapts":[75],"Biedl's":[76],"recursive":[77],"bar":[78],"construction":[79],"using":[80],"nonintegral":[81],"heights":[82],"applies":[84],"height-preserving":[86],"straightening":[87],"theorem.":[88]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}
