{"id":"https://openalex.org/W4387265389","doi":"https://doi.org/10.1017/s0963548323000317","title":"Many Hamiltonian subsets in large graphs with given density","display_name":"Many Hamiltonian subsets in large graphs with given density","publication_year":2023,"publication_date":"2023-10-02","ids":{"openalex":"https://openalex.org/W4387265389","doi":"https://doi.org/10.1017/s0963548323000317"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548323000317","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1017/s0963548323000317","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5015029543","display_name":"Stijn Cambie","orcid":"https://orcid.org/0000-0002-2385-1137"},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]},{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE","KR"],"is_corresponding":true,"raw_author_name":"Stijn Cambie","raw_affiliation_strings":["Department of Computer Science, KU Leuven Campus Kulak-Kortrijk, Kortrijk, Belgium","Institute for Basic Science (IBS), Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-2385-1137","affiliations":[{"raw_affiliation_string":"Department of Computer Science, KU Leuven Campus Kulak-Kortrijk, Kortrijk, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Institute for Basic Science (IBS), Daejeon, South Korea","institution_ids":["https://openalex.org/I4210104335"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100776555","display_name":"Jun Gao","orcid":"https://orcid.org/0000-0002-6750-8496"},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jun Gao","raw_affiliation_strings":["Institute for Basic Science (IBS), Daejeon, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Basic Science (IBS), Daejeon, South Korea","institution_ids":["https://openalex.org/I4210104335"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100410317","display_name":"Hong Liu","orcid":"https://orcid.org/0000-0002-5735-7321"},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hong Liu","raw_affiliation_strings":["Institute for Basic Science (IBS), Daejeon, South Korea"],"raw_orcid":"https://orcid.org/0000-0002-5735-7321","affiliations":[{"raw_affiliation_string":"Institute for Basic Science (IBS), Daejeon, South Korea","institution_ids":["https://openalex.org/I4210104335"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015029543"],"corresponding_institution_ids":["https://openalex.org/I4210104335","https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":0.6696,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62908606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"33","issue":"1","first_page":"110","last_page":"120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998999834060669,"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/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/T11476","display_name":"Graph theory and applications","score":0.9937999844551086,"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":0.8249125480651855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6341174840927124},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.60065096616745},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5249987840652466},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4952007830142975},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.4793549180030823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46572133898735046},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4394621253013611},{"id":"https://openalex.org/keywords/quartic-graph","display_name":"Quartic graph","score":0.43898528814315796},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.43193772435188293},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.36999374628067017},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.21000760793685913},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04985332489013672}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8249125480651855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6341174840927124},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.60065096616745},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5249987840652466},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4952007830142975},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.4793549180030823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46572133898735046},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4394621253013611},{"id":"https://openalex.org/C199692417","wikidata":"https://www.wikidata.org/wiki/Q7269362","display_name":"Quartic graph","level":5,"score":0.43898528814315796},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.43193772435188293},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.36999374628067017},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.21000760793685913},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04985332489013672},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548323000317","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1017/s0963548323000317","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/741414","is_oa":false,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/741414","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics Probability & Computing, vol. 33 (1), (110-120)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1493850023","https://openalex.org/W1971367602","https://openalex.org/W2010688605","https://openalex.org/W2073812123","https://openalex.org/W2081157042","https://openalex.org/W2087014485","https://openalex.org/W2109542562","https://openalex.org/W2401610261","https://openalex.org/W2402589028","https://openalex.org/W2582264901","https://openalex.org/W2964026298","https://openalex.org/W3109168039","https://openalex.org/W3125259119","https://openalex.org/W4210756586","https://openalex.org/W4214492362","https://openalex.org/W4233273976","https://openalex.org/W4250021881","https://openalex.org/W4292262955","https://openalex.org/W4309496953","https://openalex.org/W4321230076","https://openalex.org/W4362704061","https://openalex.org/W4367046774","https://openalex.org/W4380928028","https://openalex.org/W6785020325"],"related_works":["https://openalex.org/W2377278407","https://openalex.org/W2588150626","https://openalex.org/W2527800796","https://openalex.org/W4293154719","https://openalex.org/W1957980392","https://openalex.org/W1534832295","https://openalex.org/W2057580655","https://openalex.org/W1978219832","https://openalex.org/W2319833372","https://openalex.org/W2070086094"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"set":[2],"of":[3,44,62],"vertices":[4],"in":[5],"a":[6,9,15,18,49,63,74],"graph":[7,64,70,97],"is":[8],"Hamiltonian":[10,19,45,106],"subset":[11],"if":[12],"it":[13,72],"induces":[14],"subgraph":[16],"containing":[17],"cycle.":[20],"Kim,":[21],"Liu,":[22],"Sharifzadeh,":[23],"and":[24,59],"Staden":[25],"proved":[26],"that":[27,54,91],"for":[28],"large":[29],"$d$":[30,38,101],",":[31,39],"among":[32],"all":[33],"graphs":[34],"with":[35,98],"minimum":[36,99],"degree":[37,100],"$K_{d+1}$":[40],"minimises":[41],"the":[42,57,60,79],"number":[43],"subsets.":[46,107],"We":[47],"prove":[48],"near":[50],"optimal":[51],"lower":[52],"bound":[53,77,89],"takes":[55],"also":[56],"order":[58],"structure":[61],"into":[65],"account.":[66],"For":[67],"many":[68],"natural":[69],"classes,":[71],"provides":[73],"much":[75],"better":[76],"than":[78],"extremal":[80],"one":[81],"(":[82],"$\\approx":[83],"2^{d+1}$":[84],").":[85],"Among":[86],"others,":[87],"our":[88],"implies":[90],"an":[92],"$n$":[93],"-vertex":[94],"$C_4$":[95],"-free":[96],"contains":[102],"at":[103],"least":[104],"$n2^{d^{2-o(1)}}$":[105]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}
