{"id":"https://openalex.org/W1490824980","doi":"https://doi.org/10.37236/1055","title":"Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size","display_name":"Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size","publication_year":2006,"publication_date":"2006-03-31","ids":{"openalex":"https://openalex.org/W1490824980","doi":"https://doi.org/10.37236/1055","mag":"1490824980"},"language":"en","primary_location":{"id":"doi:10.37236/1055","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1055","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r29/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/v13i1r29/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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"]},{"id":"https://openalex.org/I195575238","display_name":"Middlebury College","ror":"https://ror.org/0217hb928","country_code":"US","type":"education","lineage":["https://openalex.org/I195575238"]},{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL","US"],"is_corresponding":false,"raw_author_name":"Ronald Gould","raw_affiliation_strings":["Department of Mathematics Middlebury College Middlebury, VT 05753","Department of Discrete Mathematics Faculty of Mathematics and CS Adam Mickiewicz University Poznan, Poland","Department of Mathematics and Computer Science 400 Dowman Drive Emory University, Atlanta GA 30322"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Middlebury College Middlebury, VT 05753","institution_ids":["https://openalex.org/I195575238"]},{"raw_affiliation_string":"Department of Discrete Mathematics Faculty of Mathematics and CS Adam Mickiewicz University Poznan, Poland","institution_ids":["https://openalex.org/I59411706"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science 400 Dowman Drive Emory University, Atlanta GA 30322","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003433063","display_name":"Tomasz \u0141uczak","orcid":"https://orcid.org/0000-0002-3517-9034"},"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"]},{"id":"https://openalex.org/I195575238","display_name":"Middlebury College","ror":"https://ror.org/0217hb928","country_code":"US","type":"education","lineage":["https://openalex.org/I195575238"]},{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL","US"],"is_corresponding":false,"raw_author_name":"Tomasz \u0141uczak","raw_affiliation_strings":["Department of Discrete Mathematics Faculty of Mathematics and CS Adam Mickiewicz University Poznan, Poland","Department of Mathematics and Computer Science 400 Dowman Drive Emory University, Atlanta GA 30322","Department of Mathematics Middlebury College Middlebury, VT 05753"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Discrete Mathematics Faculty of Mathematics and CS Adam Mickiewicz University Poznan, Poland","institution_ids":["https://openalex.org/I59411706"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science 400 Dowman Drive Emory University, Atlanta GA 30322","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"Department of Mathematics Middlebury College Middlebury, VT 05753","institution_ids":["https://openalex.org/I195575238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034811194","display_name":"John R. Schmitt","orcid":null},"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"]},{"id":"https://openalex.org/I195575238","display_name":"Middlebury College","ror":"https://ror.org/0217hb928","country_code":"US","type":"education","lineage":["https://openalex.org/I195575238"]},{"id":"https://openalex.org/I59411706","display_name":"Adam Mickiewicz University in Pozna\u0144","ror":"https://ror.org/04g6bbq64","country_code":"PL","type":"education","lineage":["https://openalex.org/I59411706"]}],"countries":["PL","US"],"is_corresponding":false,"raw_author_name":"John Schmitt","raw_affiliation_strings":["Department of Mathematics and Computer Science 400 Dowman Drive Emory University, Atlanta GA 30322","Department of Discrete Mathematics Faculty of Mathematics and CS Adam Mickiewicz University Poznan, Poland","Department of Mathematics Middlebury College Middlebury, VT 05753"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science 400 Dowman Drive Emory University, Atlanta GA 30322","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"Department of Discrete Mathematics Faculty of Mathematics and CS Adam Mickiewicz University Poznan, Poland","institution_ids":["https://openalex.org/I59411706"]},{"raw_affiliation_string":"Department of Mathematics Middlebury College Middlebury, VT 05753","institution_ids":["https://openalex.org/I195575238"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8799,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.81868365,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11476","display_name":"Graph theory and applications","score":0.9991000294685364,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9988999962806702,"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":0.8454475402832031},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8362985849380493},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6503243446350098},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5705369710922241},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.47822803258895874},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.45114466547966003},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42732322216033936},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4193251430988312},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05173024535179138}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8454475402832031},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8362985849380493},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6503243446350098},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5705369710922241},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.47822803258895874},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.45114466547966003},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42732322216033936},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4193251430988312},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05173024535179138},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1055","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1055","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r29/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:10.1.1.706.1539","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.706.1539","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://community.middlebury.edu/%7Ejschmitt/papers/EJC_cyclesaturated_1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.83.482","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.83.482","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r29.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1055","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1055","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r29/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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1490824980.pdf","grobid_xml":"https://content.openalex.org/works/W1490824980.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W80657577","https://openalex.org/W185109540","https://openalex.org/W1510730180","https://openalex.org/W1625967749","https://openalex.org/W1975405412","https://openalex.org/W1990490082","https://openalex.org/W1992511794","https://openalex.org/W2006394242","https://openalex.org/W2093497699","https://openalex.org/W2326337330","https://openalex.org/W3179424942","https://openalex.org/W6603102344","https://openalex.org/W6606449042"],"related_works":["https://openalex.org/W4311883357","https://openalex.org/W94411513","https://openalex.org/W2377770720","https://openalex.org/W2113626999","https://openalex.org/W160889949","https://openalex.org/W2364696089","https://openalex.org/W309910862","https://openalex.org/W4210637712","https://openalex.org/W2369004811","https://openalex.org/W2392500469"],"abstract_inverted_index":{"A":[0],"graph":[1,26,43],"$G$":[2,9,24],"is":[3],"said":[4],"to":[5,50],"be":[6,51],"$C_l$-saturated":[7,42],"if":[8],"contains":[10],"no":[11],"cycle":[12,31],"of":[13,23,32,38,40,69,76],"length":[14,33],"$l$,":[15],"but":[16],"for":[17,58,78],"any":[18],"edge":[19],"in":[20],"the":[21,25,74],"complement":[22],"$G+e$":[27],"does":[28],"contain":[29],"a":[30,41,67],"$l$.":[34],"The":[35],"minimum":[36],"number":[37],"edges":[39],"was":[44],"shown":[45],"by":[46],"Barefoot":[47],"et":[48],"al.":[49],"between":[52],"$n+c_1{n\\over":[53],"l}$":[54,57],"and":[55,63],"$n+c_2{n\\over":[56],"some":[59],"positive":[60],"constants":[61],"$c_1$":[62],"$c_2$.":[64],"This":[65],"confirmed":[66],"conjecture":[68],"Bollob\u00e1s.":[70],"Here":[71],"we":[72],"improve":[73],"value":[75],"$c_2$":[77],"$l":[79],"\\geq":[80],"8$.":[81]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
