{"id":"https://openalex.org/W3138268353","doi":"https://doi.org/10.37236/8903","title":"On the Strong Hanani-Tutte Theorem","display_name":"On the Strong Hanani-Tutte Theorem","publication_year":2021,"publication_date":"2021-02-26","ids":{"openalex":"https://openalex.org/W3138268353","doi":"https://doi.org/10.37236/8903","mag":"3138268353"},"language":"en","primary_location":{"id":"doi:10.37236/8903","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8903","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p43/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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p43/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008734925","display_name":"Hooman Reisi Dehkordi","orcid":"https://orcid.org/0000-0001-6031-0033"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Hooman R. Dehkordi","raw_affiliation_strings":["Faculty of Information Technology, Monash University, Clayton, Victoria 3800"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, Monash University, Clayton, Victoria 3800","institution_ids":["https://openalex.org/I56590836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005637509","display_name":"Graham Farr","orcid":null},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Graham Farr","raw_affiliation_strings":["Faculty of Information Technology Monash University Clayton, Victoria 3800, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology Monash University Clayton, Victoria 3800, Australia","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I56590836"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06751446,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9939000010490417,"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":0.9939000010490417,"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":0.9520000219345093,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.838010311126709},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.779075562953949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7701138257980347},{"id":"https://openalex.org/keywords/polyhedral-graph","display_name":"Polyhedral graph","score":0.6716060638427734},{"id":"https://openalex.org/keywords/graph-minor","display_name":"Graph minor","score":0.6367636919021606},{"id":"https://openalex.org/keywords/robertson\u2013seymour-theorem","display_name":"Robertson\u2013Seymour theorem","score":0.5402683019638062},{"id":"https://openalex.org/keywords/outerplanar-graph","display_name":"Outerplanar graph","score":0.5385813117027283},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5124631524085999},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.401711642742157},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.3392467796802521},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.21302571892738342},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.1927204728126526},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.1833433210849762},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.16247019171714783}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.838010311126709},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.779075562953949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7701138257980347},{"id":"https://openalex.org/C91233654","wikidata":"https://www.wikidata.org/wiki/Q4555371","display_name":"Polyhedral graph","level":5,"score":0.6716060638427734},{"id":"https://openalex.org/C140752511","wikidata":"https://www.wikidata.org/wiki/Q905837","display_name":"Graph minor","level":5,"score":0.6367636919021606},{"id":"https://openalex.org/C173644813","wikidata":"https://www.wikidata.org/wiki/Q3527155","display_name":"Robertson\u2013Seymour theorem","level":5,"score":0.5402683019638062},{"id":"https://openalex.org/C125792925","wikidata":"https://www.wikidata.org/wiki/Q3115604","display_name":"Outerplanar graph","level":5,"score":0.5385813117027283},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5124631524085999},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.401711642742157},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.3392467796802521},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.21302571892738342},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.1927204728126526},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.1833433210849762},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.16247019171714783}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/8903","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8903","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p43/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:monash.edu:openaire/c80788e8-ab5e-4336-b0b6-d82f4f58e9c3","is_oa":true,"landing_page_url":"https://research.monash.edu/en/publications/c80788e8-ab5e-4336-b0b6-d82f4f58e9c3","pdf_url":null,"source":{"id":"https://openalex.org/S4306402625","display_name":"Monash University Research Portal (Monash University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I56590836","host_organization_name":"Monash University","host_organization_lineage":["https://openalex.org/I56590836"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Dehkordi, H R & Farr, G 2021, 'On the strong Hanani-Tutte Theorem', The Electronic Journal of Combinatorics, vol. 28, no. 1, P1.43. https://doi.org/10.37236/8903","raw_type":"article"},{"id":"pmh:oai:monash.edu:publications/c80788e8-ab5e-4336-b0b6-d82f4f58e9c3","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85101513292&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4306402625","display_name":"Monash University Research Portal (Monash University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I56590836","host_organization_name":"Monash University","host_organization_lineage":["https://openalex.org/I56590836"],"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":"Dehkordi , H R & Farr , G 2021 , ' On the strong Hanani-Tutte Theorem ' , Electronic Journal of Combinatorics , vol. 28 , no. 1 , P1.43 . https://doi.org/10.37236/8903","raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/8903","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8903","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p43/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/W3138268353.pdf","grobid_xml":"https://content.openalex.org/works/W3138268353.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1563334952","https://openalex.org/W1969190443","https://openalex.org/W1973059108","https://openalex.org/W2025868128","https://openalex.org/W2058825457","https://openalex.org/W2058955254","https://openalex.org/W2112319409","https://openalex.org/W2751054776","https://openalex.org/W2962876363","https://openalex.org/W2963132380","https://openalex.org/W3099172058","https://openalex.org/W3119883127","https://openalex.org/W4254021853","https://openalex.org/W6649182536","https://openalex.org/W6676467219","https://openalex.org/W6730074882"],"related_works":["https://openalex.org/W2968633427","https://openalex.org/W2963028755","https://openalex.org/W3183510330","https://openalex.org/W2054860235","https://openalex.org/W2885367267","https://openalex.org/W2078415120","https://openalex.org/W3138268353","https://openalex.org/W2532416299","https://openalex.org/W2963883839","https://openalex.org/W2154104378"],"abstract_inverted_index":{"A":[0,43],"graph":[1,21,44,50,145],"is":[2,22,46,146],"planar":[3,23,49,97,123,140,147],"if":[4,24,51,148],"it":[5,25,52,149,166],"has":[6,26,53,150,167],"a":[7,20,27,47,54,107,117,131,144,151,168,173],"drawing":[8,28,55,152],"in":[9,35,64,82,94,153],"which":[10,154],"no":[11],"two":[12,33,74,156],"edges":[13,34,60,158],"cross.":[14],"The":[15],"Hanani-Tutte":[16,118,137],"Theorem":[17,138],"states":[18],"that":[19,31,58,79,143,171],"$D$":[29,36,56],"such":[30,57],"any":[32,69,73,155],"cross":[37,63,159],"an":[38,160],"even":[39,161],"number":[40,162],"of":[41,92,134,163,176],"times.":[42],"$G$":[45],"non-separating":[48,122],"(1)":[59],"do":[61],"not":[62,81],"$D$,":[65],"and":[66,72,77,85,104],"(2)":[67],"for":[68,121,139],"cycle":[70,170],"$C$":[71,93],"vertices":[75],"$u$":[76,84],"$v$":[78,86],"are":[80,87,99],"$C$,":[83],"on":[88],"the":[89,135,177],"same":[90],"side":[91],"$D$.":[95],"Non-separating":[96],"graphs":[98],"closed":[100],"under":[101],"taking":[102],"minors":[103],"hence":[105],"have":[106],"finite":[108],"forbidden":[109],"minor":[110],"characterisation.":[111],"In":[112],"this":[113,127],"paper,":[114],"we":[115],"prove":[116,130],"type":[119],"theorem":[120,128],"graphs.":[124],"We":[125],"use":[126],"to":[129],"stronger":[132],"version":[133],"strong":[136],"graphs,":[141],"namely":[142],"disjoint":[157],"times":[164],"or":[165],"chordless":[169],"enables":[172],"suitable":[174],"decomposition":[175],"graph.":[178]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}