{"id":"https://openalex.org/W7207578512","doi":"https://doi.org/10.48550/arxiv.2609.01989","title":"Rainbow Berge Hamiltonicity in edge-colored random $k$-uniform hypergraphs","display_name":"Rainbow Berge Hamiltonicity in edge-colored random $k$-uniform hypergraphs","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207578512","doi":"https://doi.org/10.48550/arxiv.2609.01989"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01989","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01989","pdf_url":"https://arxiv.org/pdf/2609.01989","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.01989","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140369777","display_name":"Liping Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Liping","raw_affiliation_strings":["Center for Discrete Mathematics , Fuzhou University , Fujian , 350108 , P. R China","School of Mathematics and Statistics , Fuzhou University , Fujian , 350108 , P. R China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Discrete Mathematics , Fuzhou University , Fujian , 350108 , P. R China","institution_ids":["https://openalex.org/I80947539"]},{"raw_affiliation_string":"School of Mathematics and Statistics , Fuzhou University , Fujian , 350108 , P. R China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102020531","display_name":"Ailian Chen","orcid":"https://orcid.org/0000-0003-2750-7605","observed_orcids":["https://orcid.org/0000-0003-2750-7605"]},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Ailian","raw_affiliation_strings":["School of Mathematics and Statistics , Fuzhou University , Fujian , 350108 , P. R China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Fuzhou University , Fujian , 350108 , P. R China","institution_ids":["https://openalex.org/I80947539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I80947539"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":1.0,"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":1.0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0,"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/T11166","display_name":"Analytic Number Theory Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/k-uniform-hypergraphs","display_name":"k-uniform hypergraphs","score":0.8740000128746033},{"id":"https://openalex.org/keywords/hamiltonicity","display_name":"Hamiltonicity","score":0.7170000076293945},{"id":"https://openalex.org/keywords/rainbow-subgraphs","display_name":"rainbow subgraphs","score":0.878000020980835},{"id":"https://openalex.org/keywords/threshold-probability","display_name":"threshold probability","score":0.5139999985694885},{"id":"https://openalex.org/keywords/asymptotic-tightness","display_name":"asymptotic tightness","score":0.7860000133514404},{"id":"https://openalex.org/keywords/random-graphs","display_name":"random graphs","score":0.4860000014305115}],"concepts":[{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.8532000184059143},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8277999758720398},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8022000193595886},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7111999988555908},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5328999757766724},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.45089998841285706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43950000405311584},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38089999556541443},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.36820000410079956},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.30079999566078186},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01989","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01989","pdf_url":"https://arxiv.org/pdf/2609.01989","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.01989","doi":"https://doi.org/10.48550/arxiv.2609.01989","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01989","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.01989","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01989","pdf_url":"https://arxiv.org/pdf/2609.01989","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1810861467","display_name":null,"funder_award_id":"11401102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7194473695","display_name":null,"funder_award_id":"11671088","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207578512.pdf","grobid_xml":"https://content.openalex.org/works/W7207578512.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2751702261","https://openalex.org/W2279529641","https://openalex.org/W2949631368","https://openalex.org/W2950022103","https://openalex.org/W1490972901","https://openalex.org/W4319048557","https://openalex.org/W7111315772","https://openalex.org/W2535840617","https://openalex.org/W7099242351","https://openalex.org/W2093446084"],"abstract_inverted_index":{"Let":[0],"$H":[1,73,140],"\\sim":[2,74,141],"H^{k}_c(n,p)$":[3,142],"be":[4],"an":[5],"edge-colored":[6,70],"random":[7,71,102],"$k$-uniform":[8,103],"hypergraph":[9],"on":[10,152],"the":[11,36,69,90,93,110],"vertex":[12],"set":[13,38],"$[n]$,":[14],"where":[15],"each":[16],"edge":[17],"$e":[18],"\\in":[19],"\\binom{[n]}{k}$":[20],"is":[21,28],"included":[22],"independently":[23,31],"with":[24,66,137],"probability":[25,68,139],"$p$":[26,155],"and":[27,30,45,54,86,125,154],"uniformly":[29],"assigned":[32],"a":[33,77,96,144],"color":[34,37],"from":[35],"$[c]$.":[39],"For":[40],"$k":[41,115],"=":[42,52,56,123,127],"2$,":[43],"Ferber":[44],"Krivelevich":[46],"(2016)":[47],"established":[48],"that":[49,120],"if":[50,121],"$c":[51,122],"(1+o(1))n$":[53,124],"$p":[55,126],"(\\log":[57],"n":[58,62,130,133],"+":[59,63,131,134],"\\log":[60,61],"\u03c9(n))/n$,":[64],"then":[65,136],"high":[67,138],"graph":[72],"H^2_c(n,p)$":[75],"contains":[76,143],"rainbow":[78,145],"Hamilton":[79,98,146],"Berge":[80,99,147,164],"cycle.":[81,148],"Subsequently,":[82],"Bal,":[83],"Berkowitz,":[84],"Devlin,":[85],"Schacht":[87],"(2021)":[88],"determined":[89],"threshold":[91],"for":[92],"appearance":[94],"of":[95],"(non-rainbow)":[97],"cycle":[100],"in":[101],"hypergraphs.":[104],"In":[105],"this":[106],"paper,":[107],"we":[108],"generalize":[109],"results":[111],"to":[112],"all":[113],"integers":[114],"\\ge":[116],"3$.":[117],"We":[118],"prove":[119],"(k-1)!":[128],"\\frac{\\log":[129],"\\log\\log":[132],"\u03c9(n)}{n^{k-1}}$,":[135],"Furthermore,":[149],"both":[150],"conditions":[151],"$c$":[153],"are":[156],"asymptotically":[157],"tight.":[158],"\\noindent\\emph{Key":[159],"words:}":[160],"Rainbow":[161],"subgraph,":[162],"Hamiltonicity,":[163],"cycle,":[165],"Random":[166],"hypergraph.":[167]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-04T00:00:00"}