{"id":"https://openalex.org/W4393034806","doi":"https://doi.org/10.37236/11670","title":"An Asymptotically Sharp Bound on the Maximum Number of Independent Transversals","display_name":"An Asymptotically Sharp Bound on the Maximum Number of Independent Transversals","publication_year":2024,"publication_date":"2024-03-21","ids":{"openalex":"https://openalex.org/W4393034806","doi":"https://doi.org/10.37236/11670"},"language":"en","primary_location":{"id":"doi:10.37236/11670","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11670","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i1p68/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/v31i1p68/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058682726","display_name":"Jake Ruotolo","orcid":null},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jake Ruotolo","raw_affiliation_strings":["Harvard University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard University","institution_ids":["https://openalex.org/I2801851002"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100413965","display_name":"Kevin Wang","orcid":"https://orcid.org/0009-0003-4227-7745"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kevin Wang","raw_affiliation_strings":["University of Iowa"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Iowa","institution_ids":["https://openalex.org/I126307644"]}]},{"author_position":"last","author":{"id":null,"display_name":"Fan Wei","orcid":null},"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":"Fan Wei","raw_affiliation_strings":["Princeton University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Princeton University","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04412695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9878000020980835,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9878000020980835,"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/T12029","display_name":"DNA and Biological Computing","score":0.9702000021934509,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9544000029563904,"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/mathematics","display_name":"Mathematics","score":0.9147818088531494},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7891638278961182},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.486812561750412},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37292659282684326},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.060393333435058594}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9147818088531494},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7891638278961182},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.486812561750412},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37292659282684326},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.060393333435058594}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/11670","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11670","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i1p68/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"}],"best_oa_location":{"id":"doi:10.37236/11670","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/11670","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i1p68/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":[{"id":"https://openalex.org/G1109628387","display_name":"On Regularity Methods and Applications in Graph Theory","funder_award_id":"1953958","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8158035576","display_name":"REU Site: New York City Discrete Mathematics REU","funder_award_id":"2051026","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8950083208","display_name":null,"funder_award_id":"DMS-1953958","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G979147645","display_name":null,"funder_award_id":"DMS 2051026","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4393034806.pdf"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4213174622"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885","https://openalex.org/W2963966623"],"abstract_inverted_index":{"Let":[0,13],"$G$":[1,32],"be":[2],"a":[3],"multipartite":[4],"graph":[5],"with":[6,33],"partition":[7],"$V_1,":[8],"V_2,\\ldots,":[9],"V_k$":[10],"of":[11,19,31,54],"$V(G)$.":[12],"$d_{i,j}$":[14],"denote":[15],"the":[16,20,51,58],"edge":[17],"density":[18],"pair":[21],"$(V_i,":[22],"V_j)$.":[23],"An":[24],"independent":[25,29,55],"transversal":[26],"is":[27],"an":[28,45],"set":[30],"exactly":[34],"one":[35],"vertex":[36],"in":[37],"each":[38],"$V_i$.":[39],"In":[40],"this":[41],"paper,":[42],"we":[43],"prove":[44],"asymptotically":[46],"sharp":[47],"upper":[48],"bound":[49],"on":[50],"maximum":[52],"number":[53],"transversals":[56],"given":[57],"$d_{i,j}$'s.":[59]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
