{"id":"https://openalex.org/W3211309039","doi":"https://doi.org/10.1137/21m1456509","title":"Pure Pairs. IX. Transversal Trees","display_name":"Pure Pairs. IX. Transversal Trees","publication_year":2024,"publication_date":"2024-02-02","ids":{"openalex":"https://openalex.org/W3211309039","doi":"https://doi.org/10.1137/21m1456509","mag":"3211309039"},"language":"en","primary_location":{"id":"doi:10.1137/21m1456509","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1456509","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2111.00532","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045091550","display_name":"Alex Scott","orcid":"https://orcid.org/0000-0003-4489-5988"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Alex Scott","raw_affiliation_strings":["Mathematical Institute, University of Oxford, Oxford, OX2 6GG UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031948088","display_name":"Paul Seymour","orcid":"https://orcid.org/0000-0003-0067-4534"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Seymour","raw_affiliation_strings":["Department of Mathematics, Princeton University, Princeton, NJ 08544 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton University, Princeton, NJ 08544 USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003940613","display_name":"Sophie Spirkl","orcid":"https://orcid.org/0000-0002-2536-5618"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sophie T. Spirkl","raw_affiliation_strings":["University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada"],"raw_orcid":"https://orcid.org/0000-0002-2536-5618","affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045091550"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01150705,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"1","first_page":"645","last_page":"667"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":1.0,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/combinatorics","display_name":"Combinatorics","score":0.8728359341621399},{"id":"https://openalex.org/keywords/transversal","display_name":"Transversal (combinatorics)","score":0.7775229811668396},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6834564208984375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6376678347587585},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6280233860015869},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6170660853385925},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.48216360807418823},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4330425560474396},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37985163927078247}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8728359341621399},{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.7775229811668396},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6834564208984375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6376678347587585},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6280233860015869},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6170660853385925},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.48216360807418823},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4330425560474396},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37985163927078247},{"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:10.1137/21m1456509","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1456509","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2111.00532","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.00532","pdf_url":"https://arxiv.org/pdf/2111.00532","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:e53a9669-01dc-471b-b240-45cc97bb8371","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:e53a9669-01dc-471b-b240-45cc97bb8371","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"pmh:oai:uwspace.uwaterloo.ca:10012/20340","is_oa":true,"landing_page_url":"http://hdl.handle.net/10012/20340","pdf_url":null,"source":{"id":"https://openalex.org/S4306401661","display_name":"UWSpace (University of Waterloo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I151746483","host_organization_name":"University of Waterloo","host_organization_lineage":["https://openalex.org/I151746483"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2111.00532","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.00532","pdf_url":"https://arxiv.org/pdf/2111.00532","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1348714323","display_name":null,"funder_award_id":"DMS-1800053","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2146822515","display_name":null,"funder_award_id":"DMS-2154169","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5709578813","display_name":"Local-Global Interactions in Combinatorics","funder_award_id":"EP/V007327/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7461889428","display_name":null,"funder_award_id":"FA9550-22-1-0234","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7555595301","display_name":null,"funder_award_id":"EP/V007327/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G823600699","display_name":null,"funder_award_id":"A9550-19-1-0187","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1495916036","https://openalex.org/W1984080039","https://openalex.org/W2034681107","https://openalex.org/W2790872309","https://openalex.org/W2892310954","https://openalex.org/W2893140165","https://openalex.org/W2893779750","https://openalex.org/W2894017597","https://openalex.org/W2962706453","https://openalex.org/W2978963187","https://openalex.org/W3010457833","https://openalex.org/W3082032630","https://openalex.org/W3127936178","https://openalex.org/W4240666298"],"related_works":["https://openalex.org/W2271112932","https://openalex.org/W2772332644","https://openalex.org/W4251387394","https://openalex.org/W2222693213","https://openalex.org/W2167396658","https://openalex.org/W2952258011","https://openalex.org/W2015634066","https://openalex.org/W2188987556","https://openalex.org/W3046629113","https://openalex.org/W2048339306"],"abstract_inverted_index":{"&lt;p&gt;Fix":[0],"&lt;em&gt;k&lt;/em&gt;&amp;gt;0,":[1],"and":[2,72,94,104],"let&amp;nbsp;&lt;em&gt;G&lt;/em&gt;":[3],"be":[4,114],"a":[5,53,87,110],"graph,":[6],"with":[7],"vertex":[8,36],"set":[9],"partitioned":[10],"into":[11],"&lt;em&gt;k&lt;/em&gt;":[12,45],"subsets":[13,58],"(&amp;ldquo;blocks&amp;rdquo;)":[14],"of":[15,22,56,59,84,89,91,119],"approximately":[16],"equal":[17],"size.":[18],"An":[19],"induced":[20],"subgraph":[21],"&lt;em&gt;G&lt;/em&gt;":[23,51],"is":[24,52,86],"&amp;ldquo;transversal&amp;rdquo;":[25],"(with":[26],"respect":[27],"to":[28],"this":[29],"partition)":[30],"if":[31,116],"it":[32,42],"has":[33,43],"exactly":[34,44],"one":[35,90],"in":[37,50,73,80],"each":[38,83],"block":[39],"(and":[40],"therefore":[41],"vertices).":[46],"A":[47],"&amp;ldquo;pure":[48],"pair&amp;rdquo;":[49],"pair":[54,112],"&lt;em&gt;X&lt;/em&gt;,&lt;em&gt;Y&lt;/em&gt;":[55,66,85],"disjoint":[57],"&lt;em&gt;V&lt;/em&gt;(&lt;em&gt;G&lt;/em&gt;)&amp;nbsp;such":[60],"that":[61],"either":[62],"all":[63],"edges":[64],"between":[65],"are":[67,78,122],"present":[68,75,115],"or":[69],"none":[70],"are;":[71],"the":[74,92,96],"context":[76],"we":[77],"interested":[79],"pure":[81,111],"pairs&amp;nbsp;(&lt;em&gt;X&lt;/em&gt;,&lt;em&gt;Y&lt;/em&gt;)&amp;nbsp;where":[82],"subset":[88],"blocks,":[93],"not":[95],"same":[97],"block.":[98],"This":[99],"paper":[100],"collects":[101],"several":[102],"results":[103],"open":[105],"questions":[106],"concerning":[107],"how":[108],"large":[109],"must":[113],"various":[117],"types":[118],"transversal":[120],"subgraphs":[121],"excluded.&lt;/p&gt;":[123]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
