{"id":"https://openalex.org/W4382812043","doi":"https://doi.org/10.37236/10728","title":"On the Chromatic Number in the Stochastic Block Model","display_name":"On the Chromatic Number in the Stochastic Block Model","publication_year":2023,"publication_date":"2023-06-30","ids":{"openalex":"https://openalex.org/W4382812043","doi":"https://doi.org/10.37236/10728"},"language":"en","primary_location":{"id":"doi:10.37236/10728","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/10728","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p56/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p56/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035608597","display_name":"Mikhail Isaev","orcid":"https://orcid.org/0000-0002-5703-0951"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AT","AU"],"is_corresponding":false,"raw_author_name":"Mikhail Isaev","raw_affiliation_strings":["School of Mathematics Monash University 3800 Clayton, Australia","Institute of Discrete Mathematics Graz University of Technology 8010 Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics Monash University 3800 Clayton, Australia","institution_ids":["https://openalex.org/I56590836"]},{"raw_affiliation_string":"Institute of Discrete Mathematics Graz University of Technology 8010 Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002103922","display_name":"Mihyun Kang","orcid":"https://orcid.org/0000-0001-8729-2779"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Mihyun Kang","raw_affiliation_strings":["Graz University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graz University of Technology","institution_ids":["https://openalex.org/I4092182"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.018,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68790717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"30","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9980000257492065,"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/T11716","display_name":"Random Matrices and Applications","score":0.9857000112533569,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12351","display_name":"Geometry and complex manifolds","score":0.9786999821662903,"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/mathematics","display_name":"Mathematics","score":0.8355075120925903},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.7449851036071777},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6499486565589905},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5780246257781982},{"id":"https://openalex.org/keywords/critical-graph","display_name":"Critical graph","score":0.5517211556434631},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.5153359770774841},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5017602443695068},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.49187707901000977},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4479484260082245},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4146023094654083},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14571678638458252},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.07952821254730225},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.07045677304267883}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8355075120925903},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.7449851036071777},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6499486565589905},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5780246257781982},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.5517211556434631},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.5153359770774841},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5017602443695068},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.49187707901000977},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4479484260082245},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4146023094654083},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14571678638458252},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.07952821254730225},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.07045677304267883}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/10728","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/10728","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p56/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"}],"best_oa_location":{"id":"doi:10.37236/10728","is_oa":true,"landing_page_url":"http://dx.doi.org/10.37236/10728","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p56/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/G5159433005","display_name":"Random Graphs: Cores, Colourings and Contagion","funder_award_id":"I3747","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4382812043.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W273178449","https://openalex.org/W1975058386","https://openalex.org/W1978161421","https://openalex.org/W2007612705","https://openalex.org/W2013490265","https://openalex.org/W2037787045","https://openalex.org/W2060664509","https://openalex.org/W2069226351","https://openalex.org/W2079330337","https://openalex.org/W2082249316","https://openalex.org/W2111559003","https://openalex.org/W2164437357","https://openalex.org/W2166965860","https://openalex.org/W2336317531","https://openalex.org/W2560864178","https://openalex.org/W2602671714","https://openalex.org/W2781377992","https://openalex.org/W2900103943","https://openalex.org/W2963535564","https://openalex.org/W2990840955","https://openalex.org/W3018106679","https://openalex.org/W3043029749","https://openalex.org/W3103904697","https://openalex.org/W3143219376","https://openalex.org/W4221157206","https://openalex.org/W4235381916","https://openalex.org/W4246845192"],"related_works":["https://openalex.org/W2562183448","https://openalex.org/W1984098916","https://openalex.org/W2046610653","https://openalex.org/W2168180506","https://openalex.org/W2057367302","https://openalex.org/W2091414672","https://openalex.org/W2891101917","https://openalex.org/W2951887113","https://openalex.org/W4390486240","https://openalex.org/W2049992750"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2],"generalisation":[3],"of":[4,11,15,31,64],"Bollob\u00e1s'":[5],"classical":[6],"result":[7],"on":[8,48],"the":[9,12,16,21,29,37,41,49,52,65],"asymptotics":[10],"chromatic":[13,38],"number":[14,30,39],"binomial":[17],"random":[18,66],"graph":[19],"to":[20,33,61],"stochastic":[22],"block":[23],"model.":[24,43],"In":[25],"addition,":[26],"by":[27],"allowing":[28],"blocks":[32],"grow,":[34],"we":[35],"determine":[36],"in":[40],"Chung-Lu":[42],"Our":[44],"approach":[45],"is":[46],"based":[47],"estimates":[50],"for":[51],"weighted":[53],"independence":[54],"number,":[55],"where":[56],"weights":[57],"are":[58],"specifically":[59],"designed":[60],"encapsulate":[62],"inhomogeneities":[63],"graph.":[67]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
