{"id":"https://openalex.org/W1596315523","doi":"https://doi.org/10.37236/1177","title":"On the Number of Hamilton Cycles in Pseudo-Random Graphs","display_name":"On the Number of Hamilton Cycles in Pseudo-Random Graphs","publication_year":2012,"publication_date":"2012-01-21","ids":{"openalex":"https://openalex.org/W1596315523","doi":"https://doi.org/10.37236/1177","mag":"1596315523"},"language":"en","primary_location":{"id":"doi:10.37236/1177","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1177","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p25/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/v19i1p25/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008556299","display_name":"Michael Krivelevich","orcid":"https://orcid.org/0000-0003-2357-4982"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel","Tel-Aviv  University"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, 69978, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel-Aviv  University","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008556299"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":4.9245,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.95354378,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"1","first_page":null,"last_page":null},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9991999864578247,"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":0.996999979019165,"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":0.8607553839683533},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8578999042510986},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.7846270203590393},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5848791003227234},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5724809765815735},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.44874119758605957},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32983890175819397},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09843957424163818},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.04574030637741089}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8607553839683533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8578999042510986},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7846270203590393},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5848791003227234},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5724809765815735},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.44874119758605957},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32983890175819397},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09843957424163818},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.04574030637741089}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1177","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1177","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p25/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:10.37236/1177","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1177","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p25/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":[],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1596315523.pdf","grobid_xml":"https://content.openalex.org/works/W1596315523.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1639593279","https://openalex.org/W1965652541","https://openalex.org/W2000252962","https://openalex.org/W2009232680","https://openalex.org/W2010688605","https://openalex.org/W2018047324","https://openalex.org/W2037114373","https://openalex.org/W2050140567","https://openalex.org/W2052478317","https://openalex.org/W2066182228","https://openalex.org/W2068871408","https://openalex.org/W2100057426","https://openalex.org/W2122689704","https://openalex.org/W2125752997","https://openalex.org/W2136219960","https://openalex.org/W2140606499","https://openalex.org/W2144068157","https://openalex.org/W2146774612","https://openalex.org/W2905110430","https://openalex.org/W2951685678","https://openalex.org/W3144881883","https://openalex.org/W4233896336"],"related_works":["https://openalex.org/W2951695430","https://openalex.org/W4300891849","https://openalex.org/W2318687609","https://openalex.org/W91590591","https://openalex.org/W159772521","https://openalex.org/W2950100995","https://openalex.org/W3170064006","https://openalex.org/W2281582664","https://openalex.org/W2554039769","https://openalex.org/W2806574890"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2],"if":[3],"$G$":[4,47],"is":[5,48],"an":[6],"$(n,d,\\lambda)$-graph":[7],"(a":[8],"$d$-regular":[9],"graph":[10],"on":[11],"$n$":[12],"vertices,":[13],"all":[14],"of":[15,43],"whose":[16],"non-trivial":[17],"eigenvalues":[18],"are":[19,27],"at":[20],"most":[21],"$\\lambda)$":[22],"and":[23],"the":[24,41],"following":[25],"conditions":[26],"satisfied:$\\frac{d}{\\lambda}\\ge":[28],"(\\log":[29],"n)^{1+\\epsilon}$":[30],"for":[31],"some":[32],"constant":[33],"$\\epsilon>0$;":[34],"$\\log":[35],"d\\cdot":[36],"\\log\\frac{d}{\\lambda}\\gg":[37],"\\log":[38],"n$,":[39],"then":[40],"number":[42],"Hamilton":[44],"cycles":[45],"in":[46],"$n!\\left(\\frac{d}{n}\\right)^n(1+o(1))^n$.":[49]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}