{"id":"https://openalex.org/W2490772428","doi":"https://doi.org/10.1080/10586458.2017.1306813","title":"On the Minimum Number of Hamiltonian Cycles in Regular Graphs","display_name":"On the Minimum Number of Hamiltonian Cycles in Regular Graphs","publication_year":2017,"publication_date":"2017-04-03","ids":{"openalex":"https://openalex.org/W2490772428","doi":"https://doi.org/10.1080/10586458.2017.1306813","mag":"2490772428"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2017.1306813","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1306813","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","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/A5046620111","display_name":"Michael Haythorpe","orcid":"https://orcid.org/0000-0001-8143-6583"},"institutions":[{"id":"https://openalex.org/I169541294","display_name":"Flinders University","ror":"https://ror.org/01kpzv902","country_code":"AU","type":"education","lineage":["https://openalex.org/I169541294"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"M. Haythorpe","raw_affiliation_strings":["School of Computer Science, Engineering and Mathematics, Flinders University, Tonsley, Australia"],"raw_orcid":"https://orcid.org/0000-0001-8143-6583","affiliations":[{"raw_affiliation_string":"School of Computer Science, Engineering and Mathematics, Flinders University, Tonsley, Australia","institution_ids":["https://openalex.org/I169541294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5046620111"],"corresponding_institution_ids":["https://openalex.org/I169541294"],"apc_list":null,"apc_paid":null,"fwci":0.4383,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.63668313,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"27","issue":"4","first_page":"426","last_page":"430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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":0.9991999864578247,"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/T10849","display_name":"Finite Group Theory Research","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8747668266296387},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7599977254867554},{"id":"https://openalex.org/keywords/pancyclic-graph","display_name":"Pancyclic graph","score":0.6371569037437439},{"id":"https://openalex.org/keywords/wheel-graph","display_name":"Wheel graph","score":0.49167925119400024},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4801589846611023},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4763079881668091},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.47587624192237854},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.46450185775756836},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4554060399532318},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4425666332244873},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.4316330850124359},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.42034047842025757},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.30498409271240234},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.2589239478111267},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.16886189579963684},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06040182709693909}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8747668266296387},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7599977254867554},{"id":"https://openalex.org/C166911692","wikidata":"https://www.wikidata.org/wiki/Q7130424","display_name":"Pancyclic graph","level":5,"score":0.6371569037437439},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.49167925119400024},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4801589846611023},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4763079881668091},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.47587624192237854},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.46450185775756836},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4554060399532318},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4425666332244873},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.4316330850124359},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.42034047842025757},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.30498409271240234},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.2589239478111267},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.16886189579963684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06040182709693909},{"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:10.1080/10586458.2017.1306813","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2017.1306813","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1968103577","https://openalex.org/W1969368048","https://openalex.org/W1992797912","https://openalex.org/W1995621089","https://openalex.org/W2087818742","https://openalex.org/W2104180013","https://openalex.org/W2296469570","https://openalex.org/W2315039435","https://openalex.org/W2508797883","https://openalex.org/W2792461236","https://openalex.org/W4241301040","https://openalex.org/W4253659528"],"related_works":["https://openalex.org/W2057580655","https://openalex.org/W2064737922","https://openalex.org/W4388585714","https://openalex.org/W2373602382","https://openalex.org/W2169450198","https://openalex.org/W2083864191","https://openalex.org/W2952856011","https://openalex.org/W203133463","https://openalex.org/W2319833372","https://openalex.org/W4300923140"],"abstract_inverted_index":{"A":[0],"graph":[1,7,90],"construction":[2,91],"that":[3,55,57],"produces":[4],"a":[5,44,61],"k-regular":[6,73],"on":[8,65,75],"n":[9,19,47,76,83,118],"vertices":[10,77],"for":[11,24,78,92,97],"any":[12],"choice":[13],"of":[14,33,46,69,101],"k":[15,79,85,114],"\u2a7e":[16,27,80,84,119],"3":[17],"and":[18,48,50,82,117],"=":[20,115],"m(k":[21],"+":[22,86],"1)":[23],"integer":[25],"m":[26],"2":[28],"is":[29,53,95,104],"described.":[30],"The":[31],"number":[32,68,100],"Hamiltonians":[34],"cycles":[35,71,103],"in":[36,72,110],"such":[37],"graphs":[38,74,94],"can":[39],"be":[40],"explicitly":[41],"determined":[42],"as":[43],"function":[45,59,109],"k,":[49],"empirical":[51],"evidence":[52],"provided":[54],"suggests":[56],"this":[58],"gives":[60],"tight":[62],"upper":[63],"bound":[64],"the":[66,99,107,111],"minimum":[67],"Hamiltonian":[70,102],"5":[81],"3.":[87],"An":[88],"additional":[89],"4-regular":[93],"described":[96],"which":[98],"superior":[105],"to":[106],"above":[108],"case":[112],"when":[113],"4":[116],"11.":[120]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
