{"id":"https://openalex.org/W3195869111","doi":"https://doi.org/10.1137/19m1296069","title":"Hamiltonicity of Random Graphs in the Stochastic Block Model","display_name":"Hamiltonicity of Random Graphs in the Stochastic Block Model","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3195869111","doi":"https://doi.org/10.1137/19m1296069","mag":"3195869111"},"language":"en","primary_location":{"id":"doi:10.1137/19m1296069","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296069","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete 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/A5039301099","display_name":"Michael Anastos","orcid":"https://orcid.org/0000-0001-5475-6522"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["CA","DE","US"],"is_corresponding":true,"raw_author_name":"Michael Anastos","raw_affiliation_strings":["University of Waterloo","Carnegie Mellon University","Freie Universit\u00e4t Berlin"],"affiliations":[{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Freie Universit\u00e4t Berlin","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["CA","DE","US"],"is_corresponding":false,"raw_author_name":"Alan Frieze","raw_affiliation_strings":["Freie Universit\u00e4t Berlin","Carnegie Mellon University","University of Waterloo"],"affiliations":[{"raw_affiliation_string":"Freie Universit\u00e4t Berlin","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103230798","display_name":"Pu Gao","orcid":"https://orcid.org/0000-0002-6363-1681"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA","DE","US"],"is_corresponding":false,"raw_author_name":"Pu Gao","raw_affiliation_strings":["Carnegie Mellon University","Freie Universit\u00e4t Berlin","University of Waterloo"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Freie Universit\u00e4t Berlin","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"University of Waterloo","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039301099"],"corresponding_institution_ids":["https://openalex.org/I151746483","https://openalex.org/I74973139","https://openalex.org/I75951250"],"apc_list":null,"apc_paid":null,"fwci":0.8412,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7246929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"35","issue":"3","first_page":"1854","last_page":"1880"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9922999739646912,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9922999739646912,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.98580002784729,"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":0.98580002784729,"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":0.7908945679664612},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7634563446044922},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.685427188873291},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.552208662033081},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5465684533119202},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4914618730545044},{"id":"https://openalex.org/keywords/stochastic-block-model","display_name":"Stochastic block model","score":0.4638848900794983},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.109800785779953}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7908945679664612},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7634563446044922},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.685427188873291},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.552208662033081},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5465684533119202},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4914618730545044},{"id":"https://openalex.org/C2779982251","wikidata":"https://www.wikidata.org/wiki/Q25053762","display_name":"Stochastic block model","level":3,"score":0.4638848900794983},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.109800785779953},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1296069","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296069","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2533871239","display_name":null,"funder_award_id":"DMS1363136","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4797868072","display_name":"New directions arising from a special diffusion process on the integer lattice","funder_award_id":"1363136","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1969138958","https://openalex.org/W2085719367"],"related_works":["https://openalex.org/W2796901439","https://openalex.org/W2977688136","https://openalex.org/W4301017148","https://openalex.org/W4283448257","https://openalex.org/W4316829854","https://openalex.org/W2754525922","https://openalex.org/W3088247692","https://openalex.org/W3048055536","https://openalex.org/W3102036813","https://openalex.org/W3035149792"],"abstract_inverted_index":{"We":[0,45],"study":[1],"the":[2,5,40],"Hamiltonicity":[3],"of":[4,8],"following":[6],"model":[7,48],"a":[9,61],"random":[10],"graph.":[11],"Suppose":[12],"that":[13,34],"we":[14,38],"partition":[15],"$[n]$":[16],"into":[17],"$V_1,V_2,\\ldots,V_k$":[18],"and":[19,54],"add":[20,39],"edge":[21,41],"$\\{x,y\\}$":[22],"to":[23],"our":[24],"graph":[25],"with":[26,42],"probability":[27,43],"$p$":[28],"if":[29],"there":[30],"exists":[31],"$i$":[32],"such":[33],"$x,y\\in":[35],"V_i$.":[36],"Otherwise,":[37],"$q$.":[44],"denote":[46],"this":[47],"by":[49],"${\\mathcal":[50],"G}({\\bf":[51],"n},":[52],"p,q)$":[53],"give":[55],"tight":[56],"results":[57],"for":[58],"Hamiltonicity,":[59],"including":[60],"critical":[62],"window":[63],"analysis,":[64],"under":[65],"various":[66],"conditions.":[67]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}
