{"id":"https://openalex.org/W3005922675","doi":"https://doi.org/10.37236/9376","title":"On the Existence of Hamilton Cycles with a Periodic Pattern in a Random Digraph","display_name":"On the Existence of Hamilton Cycles with a Periodic Pattern in a Random Digraph","publication_year":2020,"publication_date":"2020-11-13","ids":{"openalex":"https://openalex.org/W3005922675","doi":"https://doi.org/10.37236/9376","mag":"3005922675"},"language":"en","primary_location":{"id":"doi:10.37236/9376","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9376","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p30/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p30/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"Alan Frieze","raw_affiliation_strings":["Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054776001","display_name":"Xavier P\u00e9rez\u2010Gim\u00e9nez","orcid":"https://orcid.org/0000-0002-7969-1136"},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xavier P\u00e9rez-Gim\u00e9nez","raw_affiliation_strings":["Department of Mathematics, University of Nebraska-Lincoln, Lincoln NE, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Nebraska-Lincoln, Lincoln NE, USA","institution_ids":["https://openalex.org/I114395901"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079925942","display_name":"Pawe\u0142 Pra\u0142at","orcid":"https://orcid.org/0000-0001-9176-8493"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Pra\u0142at","raw_affiliation_strings":["Department of Mathematics\r\nRyerson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics\r\nRyerson University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.13411258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"27","issue":"4","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":0.9991000294685364,"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":0.9991000294685364,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9939000010490417,"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/digraph","display_name":"Digraph","score":0.9494089484214783},{"id":"https://openalex.org/keywords/traverse","display_name":"Traverse","score":0.8489817380905151},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.7737234830856323},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6568408012390137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.642343282699585},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.5476837754249573},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2773110568523407},{"id":"https://openalex.org/keywords/geodesy","display_name":"Geodesy","score":0.057535380125045776},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.05524870753288269},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.046771734952926636}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.9494089484214783},{"id":"https://openalex.org/C176809094","wikidata":"https://www.wikidata.org/wiki/Q15401496","display_name":"Traverse","level":2,"score":0.8489817380905151},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.7737234830856323},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6568408012390137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.642343282699585},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.5476837754249573},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2773110568523407},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.057535380125045776},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.05524870753288269},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.046771734952926636}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9376","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9376","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p30/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.07313","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.07313","pdf_url":"https://arxiv.org/pdf/2002.07313","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3005922675","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2002.07313.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2002.07313","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2002.07313","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/9376","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9376","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p30/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G445480892","display_name":null,"funder_award_id":"DMS1661063","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G558649131","display_name":null,"funder_award_id":"DMS1661063","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3005922675.pdf","grobid_xml":"https://content.openalex.org/works/W3005922675.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1528229596","https://openalex.org/W1557925886","https://openalex.org/W2028094090","https://openalex.org/W2336317531","https://openalex.org/W2914371735","https://openalex.org/W2964335907","https://openalex.org/W6783595081"],"related_works":["https://openalex.org/W1963261367","https://openalex.org/W2130814655","https://openalex.org/W2963396141","https://openalex.org/W2952543665","https://openalex.org/W2963663072","https://openalex.org/W2963272173","https://openalex.org/W2001766673","https://openalex.org/W1615985311","https://openalex.org/W2963451354","https://openalex.org/W2023449143","https://openalex.org/W63824703","https://openalex.org/W2051681317","https://openalex.org/W2029196217","https://openalex.org/W2962880863","https://openalex.org/W3081443516","https://openalex.org/W2620108393","https://openalex.org/W2109767783","https://openalex.org/W3195369803","https://openalex.org/W2951909556","https://openalex.org/W2950009058"],"abstract_inverted_index":{"We":[0,37],"consider":[1],"Hamilton":[2,68],"cycles":[3,69],"in":[4,22,28],"the":[5,10,19,24,29,35,41,49,55,64],"random":[6],"digraph":[7],"$D_{n,m}$":[8],"where":[9],"orientation":[11,21,42],"of":[12,66],"edges":[13,25,59],"follows":[14],"a":[15,44],"pattern":[16],"other":[17,47],"than":[18,48],"trivial":[20,50],"which":[23],"are":[26,60],"oriented":[27],"same":[30],"direction":[31],"as":[32],"we":[33],"traverse":[34],"cycle.":[36],"show":[38],"that":[39],"if":[40],"forms":[43],"periodic":[45],"pattern,":[46,51],"then":[52],"approximately":[53],"half":[54],"usual":[56],"$n\\log":[57],"n$":[58],"needed":[61],"to":[62],"guarantee":[63],"existence":[65],"such":[67],"a.a.s.":[70]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}