{"id":"https://openalex.org/W1983807516","doi":"https://doi.org/10.1002/jgt.3190190312","title":"Generalized degree conditions for graphs with bounded independence number","display_name":"Generalized degree conditions for graphs with bounded independence number","publication_year":1995,"publication_date":"1995-05-01","ids":{"openalex":"https://openalex.org/W1983807516","doi":"https://doi.org/10.1002/jgt.3190190312","mag":"1983807516"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190190312","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190190312","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/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":true,"raw_author_name":"Ralph Faudree","raw_affiliation_strings":["University of Memphis Memphis, Tennessee","University of Memphis, Memphis, Tennessee"],"affiliations":[{"raw_affiliation_string":"University of Memphis Memphis, Tennessee","institution_ids":["https://openalex.org/I94658018"]},{"raw_affiliation_string":"University of Memphis, Memphis, Tennessee","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 Atlanta, Georgia","Emory University, Atlanta, Georgia"],"affiliations":[{"raw_affiliation_string":"Emory University Atlanta, Georgia","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"Emory University, Atlanta, Georgia","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007498176","display_name":"Linda Lesniak","orcid":"https://orcid.org/0000-0001-7409-6437"},"institutions":[{"id":"https://openalex.org/I177880774","display_name":"Drew University","ror":"https://ror.org/04gds4h28","country_code":"US","type":"education","lineage":["https://openalex.org/I177880774"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Linda Lesniak","raw_affiliation_strings":["Drew University Madison, New Jersey","DREW UNIVERSITY Madison, New Jersey"],"affiliations":[{"raw_affiliation_string":"Drew University Madison, New Jersey","institution_ids":["https://openalex.org/I177880774"]},{"raw_affiliation_string":"DREW UNIVERSITY Madison, New Jersey","institution_ids":["https://openalex.org/I177880774"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085623621","display_name":"Terri Lindquester","orcid":null},"institutions":[{"id":"https://openalex.org/I117979880","display_name":"Rhodes College","ror":"https://ror.org/049xfwy04","country_code":"US","type":"education","lineage":["https://openalex.org/I117979880"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Terri Lindquester","raw_affiliation_strings":["Rhodes College Memphis, Tennessee","RHODES COLLEGE\u2028Memphis, Tennessee"],"affiliations":[{"raw_affiliation_string":"Rhodes College Memphis, Tennessee","institution_ids":["https://openalex.org/I117979880"]},{"raw_affiliation_string":"RHODES COLLEGE\u2028Memphis, Tennessee","institution_ids":["https://openalex.org/I117979880"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109469173"],"corresponding_institution_ids":["https://openalex.org/I94658018"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.042,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73287121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"19","issue":"3","first_page":"397","last_page":"409"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9966999888420105,"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":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8685702085494995},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8575254678726196},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.639818012714386},{"id":"https://openalex.org/keywords/independence-number","display_name":"Independence number","score":0.6298268437385559},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.533939778804779},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.513542890548706},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.5040785074234009},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4993412494659424},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4783881902694702},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.45548099279403687},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.44255203008651733},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.42272526025772095},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.2254422903060913},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.09631291031837463},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.051648497581481934}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8685702085494995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8575254678726196},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.639818012714386},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.6298268437385559},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.533939778804779},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.513542890548706},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.5040785074234009},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4993412494659424},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4783881902694702},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.45548099279403687},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.44255203008651733},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.42272526025772095},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.2254422903060913},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.09631291031837463},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.051648497581481934},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190190312","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190190312","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":[{"id":"https://openalex.org/F4320312141","display_name":"Global Institute for Water Security, University of Saskatchewan","ror":"https://ror.org/05997db74"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1971367602","https://openalex.org/W1994517498","https://openalex.org/W2037189698","https://openalex.org/W2084408260"],"related_works":["https://openalex.org/W2185553683","https://openalex.org/W2922486178","https://openalex.org/W1964592620","https://openalex.org/W2797552901","https://openalex.org/W582575191","https://openalex.org/W2531609948","https://openalex.org/W2035294258","https://openalex.org/W4226226102","https://openalex.org/W2477388595","https://openalex.org/W1552361948"],"abstract_inverted_index":{"Abstract":[0],"We":[1,21],"consider":[2],"a":[3,24,33,40,86,99],"generalized":[4],"degree":[5,29],"condition":[6],"based":[7],"on":[8,27,35],"the":[9,12,36],"cardinality":[10],"of":[11,15,18,39,59,101],"neighborhood":[13],"union":[14],"arbitrary":[16],"sets":[17],"r":[19,68,112,141,155,171],"vertices.":[20],"show":[22],"that":[23,95],"Dirac\u2010type":[25],"bound":[26,34],"this":[28],"in":[30,49],"conjunction":[31],"with":[32,110],"independence":[37],"number":[38],"graph":[41,100],"is":[42,98,134,144,148,160,164,176],"sufficient":[43],"to":[44],"imply":[45],"certain":[46],"hamiltonian":[47,149],"properties":[48],"graphs.":[50],"For":[51],"K":[52],"1,m":[53],"\u2010free":[54],"grphs":[55],"we":[56,64],"obtain":[57],"generalizations":[58],"known":[60],"results.":[61],"In":[62],"particular":[63],"show:":[65],"Theorem.":[66],"Let":[67],"\u2265":[69,73,105,116,127,140,154,170],"1":[70,157],"and":[71,122,142,158,174],"m":[72,129],"3":[74],"be":[75],"integers.":[76],"Then":[77],"for":[78],"each":[79],"nonnegative":[80],"function":[81],"f(r,":[82,92,128],"m)":[83,109],"there":[84],"exists":[85],"constant":[87],"C":[88,121],"=":[89],"C(r,":[90],"m,":[91],"m))":[93],"such":[94],"if":[96,136,150,166],"G":[97,114,125,133,138,143,147,152,159,163,168,175],"order":[102],"n":[103,107,118],"(n":[104],"r,":[106],">":[108],"\u03b4":[111],"(":[113,117,124],")":[115,126,139,153,169],"/3)":[119],"+":[120,156,172],"\u03b2":[123],"),":[130],"then":[131],"(a)":[132],"traceable":[135],"\u03b4(":[137,151,167],"connected;":[145],"(b)":[146],"2\u2010connected;":[161],"(c)":[162],"hamiltonian\u2010connected":[165],"2":[173],"3\u2010connected.":[177],"\u00a9":[178],"1995":[179],"John":[180],"Wiley":[181],"&":[182],"Sons,":[183],"Inc.":[184]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}