{"id":"https://openalex.org/W2025903184","doi":"https://doi.org/10.1002/(sici)1097-0118(199602)21:2<242::aid-jgt15>3.0.co;2-l","title":"Essential independent sets and Hamiltonian cycles","display_name":"Essential independent sets and Hamiltonian cycles","publication_year":1996,"publication_date":"1996-02-01","ids":{"openalex":"https://openalex.org/W2025903184","doi":"https://doi.org/10.1002/(sici)1097-0118(199602)21:2<242::aid-jgt15>3.0.co;2-l","mag":"2025903184"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199602)21:2<242::aid-jgt15>3.0.co;2-l","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199602)21:2<242::aid-jgt15>3.0.co;2-l","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042737832","display_name":"Guantao Chen","orcid":"https://orcid.org/0000-0002-3118-6632"},"institutions":[{"id":"https://openalex.org/I57328836","display_name":"North Dakota State University","ror":"https://ror.org/05h1bnb22","country_code":"US","type":"education","lineage":["https://openalex.org/I57328836"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Guantao Chen","raw_affiliation_strings":["Department of Mathematics North Dakota State University Fargo, North Dakota 58105-5075","Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105-5075"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics North Dakota State University Fargo, North Dakota 58105-5075","institution_ids":["https://openalex.org/I57328836"]},{"raw_affiliation_string":"Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105-5075","institution_ids":["https://openalex.org/I57328836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061720168","display_name":"Yoshimi Egawa","orcid":null},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshimi Egawa","raw_affiliation_strings":["Department of Applied Mathematics Science University of Tokyo Shinjuku-Ku, Tokyo 162, Japan","Department of Applied Mathematics Science University of Tokyo Shinjuku-ku, Tokyo, 162 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics Science University of Tokyo Shinjuku-Ku, Tokyo 162, Japan","institution_ids":["https://openalex.org/I161296585"]},{"raw_affiliation_string":"Department of Applied Mathematics Science University of Tokyo Shinjuku-ku, Tokyo, 162 Japan","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100352246","display_name":"Xin Liu","orcid":"https://orcid.org/0000-0002-5705-0805"},"institutions":[{"id":"https://openalex.org/I84653119","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784","country_code":"TW","type":"facility","lineage":["https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Xin Liu","raw_affiliation_strings":["Institute of Applied Mathematics Academia Sinica Beijing 100080, China","Institute of Applied Mathematics,Academia Sinica,Beijing 100080,China)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics Academia Sinica Beijing 100080, China","institution_ids":[]},{"raw_affiliation_string":"Institute of Applied Mathematics,Academia Sinica,Beijing 100080,China)","institution_ids":["https://openalex.org/I84653119"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101642885","display_name":"Akira Saito","orcid":"https://orcid.org/0000-0003-4608-242X"},"institutions":[{"id":"https://openalex.org/I104946051","display_name":"Nihon University","ror":"https://ror.org/05jk51a88","country_code":"JP","type":"education","lineage":["https://openalex.org/I104946051"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akira Saito","raw_affiliation_strings":["Department of Mathematics Nihon University Sakurajosui 3-25-40 Setagaya-Ku, Tokyo 156, Japan","Department of Mathematics, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Nihon University Sakurajosui 3-25-40 Setagaya-Ku, Tokyo 156, Japan","institution_ids":["https://openalex.org/I104946051"]},{"raw_affiliation_string":"Department of Mathematics, Nihon University, Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156, Japan","institution_ids":["https://openalex.org/I104946051"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042737832"],"corresponding_institution_ids":["https://openalex.org/I57328836"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.15369898,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"2","first_page":"242","last_page":"248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9933000206947327,"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":0.9933000206947327,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9933000206947327,"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/T11567","display_name":"semigroups and automata theory","score":0.9758999943733215,"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":0.8095710873603821},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8079280853271484},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.7024046778678894},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5992639064788818},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5237635970115662},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4829122722148895},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.43486908078193665},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4312089681625366},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06045502424240112}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8095710873603821},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8079280853271484},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.7024046778678894},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5992639064788818},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5237635970115662},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4829122722148895},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.43486908078193665},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4312089681625366},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06045502424240112},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199602)21:2<242::aid-jgt15>3.0.co;2-l","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199602)21:2<242::aid-jgt15>3.0.co;2-l","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2093397072","https://openalex.org/W2075972694","https://openalex.org/W755678515","https://openalex.org/W4387272283","https://openalex.org/W2026098617","https://openalex.org/W4299647289","https://openalex.org/W1618127724","https://openalex.org/W2066235086","https://openalex.org/W2183144262","https://openalex.org/W4360764540"],"abstract_inverted_index":{"An":[0],"independent":[1,31,77],"set":[2,32],"S":[3,14,33],"of":[4,18,34,43,63,79,85,90,115],"a":[5,16,40,101,109,116],"graph":[6,42],"G":[7],"is":[8,57],"said":[9],"to":[10,112],"be":[11],"essential":[12,30,76],"if":[13,28],"has":[15],"pair":[17],"vertices":[19],"distance":[20],"two":[21],"apart":[22],"in":[23,39,87],"G.":[24],"We":[25],"prove":[26],"that":[27],"every":[29],"order":[35,44,80],"k":[36,81,86],"\u2265":[37,52],"2":[38],"k-connected":[41],"p":[45],"satisfies":[46],"max":[47],"{deg":[48],"v:v":[49],"\u03f5":[50],"S}":[51],"\u00bd":[53],"p,":[54],"then":[55],"g":[56],"hamiltonian.":[58],"This":[59],"generalizes":[60],"the":[61,75,88,91,99,113],"result":[62],"Fan":[64],"(J.":[65],"Combinatorial":[66],"Theory":[67],"B":[68],"37":[69],"(1984),":[70],"221\u2013227).":[71],"If":[72],"we":[73,94,105],"consider":[74],"sets":[78],"+":[82],"1":[83],"instead":[84],"assumption":[89],"above":[92],"statement,":[93],"can":[95,106],"no":[96],"longer":[97],"assure":[98],"existence":[100],"hamiltonian":[102],"cycle.":[103,118],"However,":[104],"still":[107],"give":[108],"lower":[110],"bound":[111],"length":[114],"longest":[117],"\u00a9":[119],"1996":[120],"John":[121],"Wiley":[122],"&":[123],"Sons,":[124],"Inc.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
