{"id":"https://openalex.org/W1576747865","doi":"https://doi.org/10.37236/180","title":"Saturation Numbers for Trees","display_name":"Saturation Numbers for Trees","publication_year":2009,"publication_date":"2009-07-24","ids":{"openalex":"https://openalex.org/W1576747865","doi":"https://doi.org/10.37236/180","mag":"1576747865"},"language":"en","primary_location":{"id":"doi:10.37236/180","is_oa":true,"landing_page_url":"https://doi.org/10.37236/180","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r91/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":null,"license_id":null,"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/v16i1r91/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044930902","display_name":"Jill Faudree","orcid":"https://orcid.org/0000-0002-7403-9456"},"institutions":[{"id":"https://openalex.org/I141472210","display_name":"University of Alaska Fairbanks","ror":"https://ror.org/01j7nq853","country_code":"US","type":"education","lineage":["https://openalex.org/I141472210"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jill Faudree","raw_affiliation_strings":["Univ. of Alaska, Fairbanks"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ. of Alaska, Fairbanks","institution_ids":["https://openalex.org/I141472210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109469173","display_name":"Ralph J. Faudree","orcid":null},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ralph J. Faudree","raw_affiliation_strings":["University of Memphis#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Memphis#TAB#","institution_ids":["https://openalex.org/I94658018"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077689134","display_name":"Ronald J. Gould","orcid":"https://orcid.org/0000-0003-0040-9511"},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald J. Gould","raw_affiliation_strings":["Emory University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Emory University","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060263835","display_name":"Michael S. Jacobson","orcid":"https://orcid.org/0000-0003-2220-8622"},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael S. Jacobson","raw_affiliation_strings":["University of Colorado, Denver"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Colorado, Denver","institution_ids":["https://openalex.org/I921990950"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1363,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.72614565,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9836999773979187,"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":0.9805999994277954,"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":0.9225478172302246},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8082289695739746},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5821280479431152},{"id":"https://openalex.org/keywords/saturation","display_name":"Saturation (graph theory)","score":0.4829806387424469},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4015757441520691}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9225478172302246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8082289695739746},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5821280479431152},{"id":"https://openalex.org/C9930424","wikidata":"https://www.wikidata.org/wiki/Q7426587","display_name":"Saturation (graph theory)","level":2,"score":0.4829806387424469},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4015757441520691}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/180","is_oa":true,"landing_page_url":"https://doi.org/10.37236/180","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r91/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.5279","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.5279","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1r91.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/180","is_oa":true,"landing_page_url":"https://doi.org/10.37236/180","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r91/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":null,"license_id":null,"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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1576747865.pdf","grobid_xml":"https://content.openalex.org/works/W1576747865.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W185109540","https://openalex.org/W606453859","https://openalex.org/W1584653855","https://openalex.org/W1963681333","https://openalex.org/W1990490082","https://openalex.org/W1992511794","https://openalex.org/W2046830126","https://openalex.org/W2097936723","https://openalex.org/W2168876485","https://openalex.org/W2612978016","https://openalex.org/W6618503222"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"For":[0],"a":[1,5,28,63,71],"fixed":[2],"graph":[3,6,64],"$H$,":[4],"$G$":[7],"is":[8,12,27,44,56],"$H$-saturated":[9,39],"if":[10],"there":[11,26],"no":[13],"copy":[14,29],"of":[15,30,38,41,60,84,92,120,136,142,150],"$H$":[16,31],"in":[17,32,62,65,107,110],"$G$,":[18],"but":[19],"for":[20,81,94,122,139,157],"any":[21],"edge":[22],"$e":[23],"\\notin":[24],"G$,":[25],"$G":[33],"+":[34],"e$.":[35],"The":[36,76,131],"collection":[37],"graphs":[40,109],"order":[42],"$n$":[43],"denoted":[45],"by":[46],"${\\bf":[47,53,66,79,96,111,124,137,151,154],"SAT}(n,H)$,":[48],"and":[49,104,133,153],"the":[50,57,140],"saturation":[51,77],"number,":[52],"sat}(n,":[54,97],"H),$":[55],"minimum":[58,134],"number":[59],"edges":[61],"SAT}(n,H)$.":[67],"Let":[68],"$T_k$":[69,106],"be":[70,87,102,116,129,146,160],"tree":[72],"on":[73],"$k$":[74],"vertices.":[75],"numbers":[78],"sat}(n,T_k)$":[80,138,152],"some":[82],"families":[83,119],"trees":[85,93,105,121,144,158],"will":[86,101,115,128,145,159],"determined":[88],"precisely.":[89],"Some":[90,148],"classes":[91],"which":[95,108,123],"T_k)":[98],"<":[99],"n$":[100,127],"identified,":[103],"SAT}(n,T_k)$":[112],"are":[113],"forests":[114],"presented.":[117,130],"Also,":[118],"sat}(n,T_k)":[125],"\\geq":[126],"maximum":[132],"values":[135],"class":[141],"all":[143],"given.":[147],"properties":[149],"SAT}":[155],"(n,T_k)$":[156],"discussed.":[161]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}