{"id":"https://openalex.org/W2062516699","doi":"https://doi.org/10.1002/jgt.3190180808","title":"On hamiltonian\u2010connected graphs","display_name":"On hamiltonian\u2010connected graphs","publication_year":1994,"publication_date":"1994-12-01","ids":{"openalex":"https://openalex.org/W2062516699","doi":"https://doi.org/10.1002/jgt.3190180808","mag":"2062516699"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190180808","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190180808","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/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":true,"raw_author_name":"Ronald J. Gould","raw_affiliation_strings":["Department Math/CS Emory University Atlanta, Georgia"],"affiliations":[{"raw_affiliation_string":"Department Math/CS Emory University Atlanta, Georgia","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070536551","display_name":"Xingxing Yu","orcid":"https://orcid.org/0000-0002-6370-3163"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xingxing Yu","raw_affiliation_strings":["Department Mathematics Georgia Institute of Technology Atlanta, Georgia"],"affiliations":[{"raw_affiliation_string":"Department Mathematics Georgia Institute of Technology Atlanta, Georgia","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077689134"],"corresponding_institution_ids":["https://openalex.org/I150468666"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18537378,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"8","first_page":"841","last_page":"860"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8471305966377258},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6949734687805176},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6274179220199585},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5852643251419067},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4997401237487793},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.43470829725265503},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.41589540243148804},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3577042520046234},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.29058125615119934},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19224771857261658}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8471305966377258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6949734687805176},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6274179220199585},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5852643251419067},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4997401237487793},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.43470829725265503},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.41589540243148804},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3577042520046234},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.29058125615119934},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19224771857261658},{"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/jgt.3190180808","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190180808","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/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1971367602","https://openalex.org/W1995948812","https://openalex.org/W2035089435","https://openalex.org/W2157647986"],"related_works":["https://openalex.org/W2384431448","https://openalex.org/W1964592620","https://openalex.org/W4205152167","https://openalex.org/W2188756358","https://openalex.org/W2226543729","https://openalex.org/W2016126876","https://openalex.org/W3189256254","https://openalex.org/W1527576459","https://openalex.org/W2035294258","https://openalex.org/W3161337494"],"abstract_inverted_index":{"Abstract":[0],"One":[1],"of":[2,37,95,127,130],"the":[3,93],"most":[4],"fundamental":[5],"results":[6,150],"concerning":[7],"paths":[8],"in":[9],"graphs":[10],"is":[11,49,92,144],"due":[12],"to":[13],"Ore:":[14],"In":[15,98,102],"a":[16,103],"graph":[17,105],"G":[18,30,45,48,65,90,106,120,140,143],",":[19,107,134],"if":[20,108],"deg":[21,24,68,109,113],"x":[22,75,80,96],"+":[23,32,112,122],"y":[25,41],"\u2267":[26,116],"|":[27,71,85,117],"V":[28,43,63,118,138],"(":[29,44,64,74,79,89,119,139],")|":[31,121],"1":[33,111,123,133],"for":[34,60,124],"all":[35],"pairs":[36],"nonadjacent":[38],"vertices":[39,131],"x,":[40],"\u2245":[42,87],"),":[46,66,141],"then":[47,142],"hamiltonian\u2010connected.":[50,145],"We":[51],"generalize":[52],"this":[53],"result":[54],"using":[55],"set":[56],"degrees.":[57],"That":[58],"is,":[59],"S":[61,69,110,114,132,135],"\u2282":[62,137],"let":[67],"=":[70,82],"x\u2245S":[72],"N":[73,78],")|,":[76],"where":[77],")":[81],"{":[83],"v":[84],"xv":[86],"E":[88],")}":[91],"neighborhood":[94],".":[97],"particular":[99],"we":[100],"show:":[101],"3\u2010connected":[104],"2":[115,136],"each":[125],"pair":[126],"distinct":[128],"2\u2010sets":[129],"Several":[146],"corollaries":[147],"and":[148],"related":[149],"are":[151],"also":[152],"discussed.":[153]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
