{"id":"https://openalex.org/W2158786496","doi":"https://doi.org/10.37236/133","title":"Rate of Convergence of the Short Cycle Distribution in Random Regular Graphs Generated by Pegging","display_name":"Rate of Convergence of the Short Cycle Distribution in Random Regular Graphs Generated by Pegging","publication_year":2009,"publication_date":"2009-03-31","ids":{"openalex":"https://openalex.org/W2158786496","doi":"https://doi.org/10.37236/133","mag":"2158786496"},"language":"en","primary_location":{"id":"doi:10.37236/133","is_oa":true,"landing_page_url":"https://doi.org/10.37236/133","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r44/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/v16i1r44/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083257155","display_name":"Pu Gao","orcid":"https://orcid.org/0000-0002-5798-8414"},"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"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Pu Gao","raw_affiliation_strings":["Department of Combinatorics and Optimization University of Waterloo, 200 University Ave W, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization University of Waterloo, 200 University Ave W, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113900323","display_name":"Nicholas Wormald","orcid":null},"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"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nicholas Wormald","raw_affiliation_strings":["Department of Combinatorics and Optimization University of Waterloo, 200 University Ave W, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization University of Waterloo, 200 University Ave W, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083257155"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.9469,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73565999,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","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":0.9991999864578247,"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":0.9991999864578247,"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":0.9990000128746033,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mixing","display_name":"Mixing (physics)","score":0.7174845933914185},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6874043941497803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6818780303001404},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.6067954301834106},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.5745794177055359},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5601285696029663},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5016992092132568},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4677213728427887},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4226626455783844},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.19369104504585266},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1782543659210205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13409042358398438},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.05670970678329468},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05237007141113281}],"concepts":[{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.7174845933914185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6874043941497803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6818780303001404},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.6067954301834106},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.5745794177055359},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5601285696029663},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5016992092132568},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4677213728427887},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4226626455783844},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.19369104504585266},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1782543659210205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13409042358398438},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.05670970678329468},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05237007141113281},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/133","is_oa":true,"landing_page_url":"https://doi.org/10.37236/133","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r44/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.174.7993","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.7993","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/%7Enwormald/papers/lowerbound.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.1711","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.1711","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1r44.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/133","is_oa":true,"landing_page_url":"https://doi.org/10.37236/133","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r44/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":[{"id":"https://openalex.org/G1304196372","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5784215521","display_name":null,"funder_award_id":"Chair","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2158786496.pdf","grobid_xml":"https://content.openalex.org/works/W2158786496.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W638149299","https://openalex.org/W1592213313","https://openalex.org/W1981927600","https://openalex.org/W2008620264","https://openalex.org/W2018934112","https://openalex.org/W2046441507","https://openalex.org/W2061118827","https://openalex.org/W2062102322","https://openalex.org/W2100158662","https://openalex.org/W2135869163","https://openalex.org/W2477953794","https://openalex.org/W2764433274","https://openalex.org/W3083259271","https://openalex.org/W4246737745","https://openalex.org/W4250665764"],"related_works":["https://openalex.org/W4243145179","https://openalex.org/W4255875982","https://openalex.org/W4244853958","https://openalex.org/W2029404707","https://openalex.org/W4285325679","https://openalex.org/W4247719608","https://openalex.org/W4237439661","https://openalex.org/W1928239295","https://openalex.org/W4242981732","https://openalex.org/W2373038869"],"abstract_inverted_index":{"The":[0,16],"pegging":[1],"algorithm":[2],"is":[3,31,57,72],"a":[4],"method":[5],"of":[6,19,22,26],"generating":[7],"large":[8],"random":[9,28],"regular":[10,29],"graphs":[11,30],"beginning":[12],"with":[13],"small":[14],"ones.":[15],"$\\epsilon$-mixing":[17,55],"time":[18,33,56],"the":[20,32,36,63,70],"distribution":[21,37],"short":[23],"cycle":[24],"counts":[25],"these":[27],"at":[34,44],"which":[35],"reaches":[38],"and":[39],"maintains":[40],"total":[41],"variation":[42],"distance":[43],"most":[45],"$\\epsilon$":[46],"from":[47],"its":[48],"limiting":[49],"distribution.":[50],"We":[51],"show":[52],"that":[53,62],"this":[54],"not":[58],"$o(\\epsilon^{-1})$.":[59],"This":[60],"demonstrates":[61],"upper":[64],"bound":[65],"$O(\\epsilon^{-1})$":[66],"proved":[67],"recently":[68],"by":[69],"authors":[71],"essentially":[73],"tight.":[74]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}