{"id":"https://openalex.org/W1953770551","doi":"https://doi.org/10.37236/550","title":"Hamiltonicity of $k$-Traceable Graphs","display_name":"Hamiltonicity of $k$-Traceable Graphs","publication_year":2011,"publication_date":"2011-03-24","ids":{"openalex":"https://openalex.org/W1953770551","doi":"https://doi.org/10.37236/550","mag":"1953770551"},"language":"en","primary_location":{"id":"doi:10.37236/550","is_oa":true,"landing_page_url":"https://doi.org/10.37236/550","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p63/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/v18i1p63/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008608687","display_name":"Frank Bullock","orcid":null},"institutions":[{"id":"https://openalex.org/I95023434","display_name":"University of KwaZulu-Natal","ror":"https://ror.org/04qzfn040","country_code":"ZA","type":"education","lineage":["https://openalex.org/I95023434"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Frank Bullock","raw_affiliation_strings":["University of KwaZulu-Natal, Westville Campus"],"affiliations":[{"raw_affiliation_string":"University of KwaZulu-Natal, Westville Campus","institution_ids":["https://openalex.org/I95023434"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066897464","display_name":"Peter Dankelmann","orcid":"https://orcid.org/0000-0003-4376-7546"},"institutions":[{"id":"https://openalex.org/I165390105","display_name":"University of South Africa","ror":"https://ror.org/048cwvf49","country_code":"ZA","type":"education","lineage":["https://openalex.org/I165390105"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Peter Dankelmann","raw_affiliation_strings":["University of South Africa, Pretoria"],"affiliations":[{"raw_affiliation_string":"University of South Africa, Pretoria","institution_ids":["https://openalex.org/I165390105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056680244","display_name":"Marietjie Frick","orcid":"https://orcid.org/0000-0002-5011-604X"},"institutions":[{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Marietjie Frick","raw_affiliation_strings":["University of Johannesburg, Johannesburg"],"affiliations":[{"raw_affiliation_string":"University of Johannesburg, Johannesburg","institution_ids":["https://openalex.org/I24027795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089473322","display_name":"Michael A. Henning","orcid":"https://orcid.org/0000-0001-8185-067X"},"institutions":[{"id":"https://openalex.org/I872945872","display_name":"University of Winnipeg","ror":"https://ror.org/02gdzyx04","country_code":"CA","type":"education","lineage":["https://openalex.org/I872945872"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michael A. Henning","raw_affiliation_strings":["University of Winnipeg, Winnipeg"],"affiliations":[{"raw_affiliation_string":"University of Winnipeg, Winnipeg","institution_ids":["https://openalex.org/I872945872"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066866313","display_name":"Ortrud R. Oellermann","orcid":"https://orcid.org/0000-0003-3520-7514"},"institutions":[{"id":"https://openalex.org/I165390105","display_name":"University of South Africa","ror":"https://ror.org/048cwvf49","country_code":"ZA","type":"education","lineage":["https://openalex.org/I165390105"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Ortrud R. Oellermann","raw_affiliation_strings":["University of South Africa, Pretoria"],"affiliations":[{"raw_affiliation_string":"University of South Africa, Pretoria","institution_ids":["https://openalex.org/I165390105"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014639430","display_name":"Susan Van Aardt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Susan Van Aardt","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5008608687"],"corresponding_institution_ids":["https://openalex.org/I95023434"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0624017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9993000030517578,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9987000226974487,"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/combinatorics","display_name":"Combinatorics","score":0.8766219019889832},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7671724557876587},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.7177313566207886},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6155695915222168},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5319986939430237},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4916842579841614},{"id":"https://openalex.org/keywords/induced-path","display_name":"Induced path","score":0.4886470437049866},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.48803797364234924},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4431791305541992},{"id":"https://openalex.org/keywords/longest-path-problem","display_name":"Longest path problem","score":0.28838059306144714},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.17808473110198975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07565554976463318}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8766219019889832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7671724557876587},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.7177313566207886},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6155695915222168},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5319986939430237},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4916842579841614},{"id":"https://openalex.org/C58228413","wikidata":"https://www.wikidata.org/wiki/Q15704639","display_name":"Induced path","level":5,"score":0.4886470437049866},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48803797364234924},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4431791305541992},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.28838059306144714},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.17808473110198975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07565554976463318},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/550","is_oa":true,"landing_page_url":"https://doi.org/10.37236/550","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p63/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"}],"best_oa_location":{"id":"doi:10.37236/550","is_oa":true,"landing_page_url":"https://doi.org/10.37236/550","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p63/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":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G3034753964","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G58356571","display_name":null,"funder_award_id":"04080","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1953770551.pdf","grobid_xml":"https://content.openalex.org/works/W1953770551.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W62558605","https://openalex.org/W603657711","https://openalex.org/W1801255175","https://openalex.org/W1971367602","https://openalex.org/W2001161770","https://openalex.org/W2013853668","https://openalex.org/W2023478138","https://openalex.org/W2063108699","https://openalex.org/W2069905179","https://openalex.org/W2491796639","https://openalex.org/W3018367310","https://openalex.org/W4244098736","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4388585714","https://openalex.org/W2163708037","https://openalex.org/W2024994163","https://openalex.org/W1968609349","https://openalex.org/W2132921321","https://openalex.org/W2036803675","https://openalex.org/W3106943288","https://openalex.org/W2464534195","https://openalex.org/W1953770551","https://openalex.org/W3130401278"],"abstract_inverted_index":{"Let":[0],"$G$":[1,9,20,30,38],"be":[2,63],"a":[3,11,26,71],"graph.":[4],"A":[5],"Hamilton":[6,27],"path":[7,12],"in":[8],"is":[10,21,31,42,78],"containing":[13],"every":[14,34],"vertex":[15],"of":[16,37,39,50,74,89],"$G$.":[17],"The":[18],"graph":[19,73],"traceable":[22],"if":[23,33],"it":[24],"contains":[25],"path,":[28],"while":[29],"$k$-traceable":[32,51,72],"induced":[35],"subgraph":[36],"order":[40,75],"$k$":[41],"traceable.":[43],"In":[44],"this":[45],"paper,":[46],"we":[47,59,84,95],"study":[48],"hamiltonicity":[49],"graphs.":[52],"For":[53,80,91],"$k":[54,81,92],"\\geq":[55],"2$":[56],"an":[57],"integer,":[58],"define":[60],"$H(k)$":[61,76],"to":[62],"the":[64,86],"largest":[65],"integer":[66],"such":[67],"that":[68,77,97],"there":[69],"exists":[70],"nonhamiltonian.":[79],"\\le":[82,99,101],"10$,":[83],"determine":[85],"exact":[87],"value":[88],"$H(k)$.":[90],"\\ge":[93],"11$,":[94],"show":[96],"$k+2":[98],"H(k)":[100],"\\frac{1}{2}(3k-5)$.":[102]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}