{"id":"https://openalex.org/W3092219661","doi":"https://doi.org/10.37236/9066","title":"The Threshold for the Full Perfect Matching Color Profile in a Random Coloring of Random Graphs","display_name":"The Threshold for the Full Perfect Matching Color Profile in a Random Coloring of Random Graphs","publication_year":2021,"publication_date":"2021-01-29","ids":{"openalex":"https://openalex.org/W3092219661","doi":"https://doi.org/10.37236/9066","mag":"3092219661"},"language":"en","primary_location":{"id":"doi:10.37236/9066","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9066","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p21/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":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p21/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086849646","display_name":"Debsoumya Chakraborti","orcid":null},"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":true,"raw_author_name":"Debsoumya Chakraborti","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021693010","display_name":"Mihir Hasabnis","orcid":null},"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":"Mihir Hasabnis","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086849646"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.6463,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58086212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","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":0.9983000159263611,"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":0.9983000159263611,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9894999861717224,"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/T11476","display_name":"Graph theory and applications","score":0.9413999915122986,"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/combinatorics","display_name":"Combinatorics","score":0.8834739923477173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7245384454727173},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6571998596191406},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5017893314361572},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.49413660168647766},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4616730213165283},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3979288339614868},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06960278749465942}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8834739923477173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7245384454727173},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6571998596191406},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5017893314361572},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.49413660168647766},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4616730213165283},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3979288339614868},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06960278749465942}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/9066","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9066","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p21/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:1910.07674","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.07674","pdf_url":"https://arxiv.org/pdf/1910.07674","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"}],"best_oa_location":{"id":"doi:10.37236/9066","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9066","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i1p21/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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3092219661.pdf","grobid_xml":"https://content.openalex.org/works/W3092219661.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W269900985","https://openalex.org/W1759514461","https://openalex.org/W1937563492","https://openalex.org/W1951087126","https://openalex.org/W1980608991","https://openalex.org/W2007550461","https://openalex.org/W2021434280","https://openalex.org/W2033652300","https://openalex.org/W2336317531","https://openalex.org/W2596788260","https://openalex.org/W2953220200","https://openalex.org/W2963272173","https://openalex.org/W2963340890","https://openalex.org/W2963989835","https://openalex.org/W3044596032","https://openalex.org/W3121789757","https://openalex.org/W6848591375"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2567825307","https://openalex.org/W1592682627","https://openalex.org/W4295762832","https://openalex.org/W2945016732","https://openalex.org/W2785998768","https://openalex.org/W2371352078","https://openalex.org/W2362975861","https://openalex.org/W2054458431","https://openalex.org/W2804963084"],"abstract_inverted_index":{"Consider":[0],"a":[1,5,13,34,59,133,152],"graph":[2,94,156],"$G$":[3,64,89,100],"with":[4,29,65,104,107],"coloring":[6],"of":[7,25,36,49,99],"its":[8],"edge":[9],"set":[10,14,24,48],"$E(G)$":[11],"from":[12],"$Q":[15],"=":[16,69,86,118,130],"\\{c_1,c_2,":[17],"\\ldots,":[18,53,77,120],"c_q\\}$.":[19],"Let":[20,74,88],"$Q_i$":[21],"be":[22,79,90],"the":[23,37,47,91,97,112,115,145,148],"all":[26,72],"edges":[27,98],"colored":[28,103,154],"$c_i$.":[30],"Recently,":[31],"Frieze":[32],"defined":[33],"notion":[35],"perfect":[38,60],"matching":[39,61],"color":[40,105],"profile":[41],"denoted":[42],"by":[43,136],"$\\mathrm{mcp}(G)$,":[44],"which":[45],"is":[46],"vectors":[50],"$(m_1,":[51],"m_2,":[52],"m_q)$":[54],"such":[55,82],"that":[56,83],"there":[57],"exists":[58],"$M$":[62],"in":[63,151],"$|Q_i":[66],"\\cap":[67],"M|":[68],"m_i$":[70],"for":[71,114,147],"$i$.":[73],"$\\alpha_1,":[75],"\\alpha_2,":[76],"\\alpha_q$":[78],"positive":[80],"constants":[81],"$\\sum_{i=1}^q":[84],"\\alpha_i":[85],"1$.":[87],"random":[92,155],"bipartite":[93],"$G_{n,n,p}$.":[95],"Suppose":[96],"are":[101],"independently":[102],"$c_i$":[106],"probability":[108],"$\\alpha_i$.":[109],"We":[110,138],"determine":[111],"threshold":[113,146],"event":[116,150],"$\\mathrm{mcp}(G)":[117],"\\{(m_1,":[119],"m_q)":[121],"\\in":[122],"[0,n]^q":[123],":":[124],"m_1":[125],"+":[126,128],"\\cdots":[127],"m_q":[129],"n\\},$":[131],"answering":[132],"question":[134],"posed":[135],"Frieze.":[137],"further":[139],"extend":[140],"our":[141],"methods":[142],"to":[143],"find":[144],"same":[149],"randomly":[153],"$G_{n,p}$.":[157]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}