{"id":"https://openalex.org/W2167810763","doi":"https://doi.org/10.37236/1581","title":"On the Domination Number of a Random Graph","display_name":"On the Domination Number of a Random Graph","publication_year":2001,"publication_date":"2001-10-11","ids":{"openalex":"https://openalex.org/W2167810763","doi":"https://doi.org/10.37236/1581","mag":"2167810763"},"language":"en","primary_location":{"id":"doi:10.37236/1581","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1581","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r37/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r37/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030573140","display_name":"Ben Wieland","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ben Wieland","raw_affiliation_strings":["Department of Mathematics University of Chicago","University of Chicago (  )"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Chicago","institution_ids":[]},{"raw_affiliation_string":"University of Chicago (  )","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081970112","display_name":"Anant P. Godbole","orcid":"https://orcid.org/0000-0001-6984-3194"},"institutions":[{"id":"https://openalex.org/I119443389","display_name":"East Tennessee State University","ror":"https://ror.org/05rfqv493","country_code":"US","type":"education","lineage":["https://openalex.org/I119443389"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anant P. Godbole","raw_affiliation_strings":["Department of Mathematics East Tennessee State University","East Tennessee State Univ"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics East Tennessee State University","institution_ids":["https://openalex.org/I119443389"]},{"raw_affiliation_string":"East Tennessee State Univ","institution_ids":["https://openalex.org/I119443389"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030573140"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":0.914,"has_fulltext":true,"cited_by_count":65,"citation_normalized_percentile":{"value":0.77493944,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"8","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994999766349792,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9993000030517578,"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/T11476","display_name":"Graph theory and applications","score":0.9926000237464905,"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":0.919450044631958},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.842036247253418},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7325520515441895},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.64188152551651},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5938194990158081},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.5524982213973999},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5292914509773254},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5274555683135986},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.45738548040390015},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14809280633926392},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.08313155174255371},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.04731371998786926}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.919450044631958},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.842036247253418},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7325520515441895},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.64188152551651},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5938194990158081},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.5524982213973999},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5292914509773254},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5274555683135986},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.45738548040390015},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14809280633926392},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.08313155174255371},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.04731371998786926},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1581","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1581","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r37/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":false,"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:dc.etsu.edu:etsu-works-20465","is_oa":false,"landing_page_url":"https://dc.etsu.edu/etsu-works/19199","pdf_url":null,"source":{"id":"https://openalex.org/S4377196424","display_name":"Digital Commons - East Tennessee State University (East Tennessee State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119443389","host_organization_name":"East Tennessee State University","host_organization_lineage":["https://openalex.org/I119443389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ETSU Faculty Works","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.22.4344","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.4344","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_8/PDF/v8i1r37.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.9578","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.9578","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_8/PostScriptfiles/v8i1r37.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1581","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1581","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v8i1r37/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":false,"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/G7197361336","display_name":"REU SITE:  Mathematical Sciences:  Discrete Random          Structures","funder_award_id":"9619889","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309369","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"},{"id":"https://openalex.org/F4320311652","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2167810763.pdf","grobid_xml":"https://content.openalex.org/works/W2167810763.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1493071618","https://openalex.org/W1494324938","https://openalex.org/W1581552469","https://openalex.org/W2068871408","https://openalex.org/W2905110430","https://openalex.org/W3144881883"],"related_works":["https://openalex.org/W2349109195","https://openalex.org/W2953046811","https://openalex.org/W2383129606","https://openalex.org/W2154705857","https://openalex.org/W2104330975","https://openalex.org/W4302804110","https://openalex.org/W2030761932","https://openalex.org/W2187055990","https://openalex.org/W1994148577","https://openalex.org/W2167810763"],"abstract_inverted_index":{"In":[0],"this":[1,28],"paper,":[2],"we":[3],"show":[4],"that":[5,55],"the":[6,31,63,80,92,98],"domination":[7,81],"number":[8,23,82],"$D$":[9],"of":[10,33],"a":[11,17,38,52,75],"random":[12],"graph":[13,65],"enjoys":[14],"as":[15,19],"sharp":[16],"concentration":[18,41,78],"does":[20],"its":[21],"chromatic":[22],"$\\chi$.":[24],"We":[25,60],"first":[26],"prove":[27,74],"fact":[29],"for":[30,47,51,79],"sequence":[32,53],"graphs":[34],"$\\{G(n,p_n\\},\\;":[35],"n\\to\\infty$,":[36],"where":[37,69],"two":[39],"point":[40,77],"is":[42,71],"obtained":[43],"with":[44,83,97],"high":[45],"probability":[46,84],"$p_n=p$":[48],"(fixed)":[49],"or":[50],"$p_n$":[54],"approaches":[56],"zero":[57],"sufficiently":[58],"slowly.":[59],"then":[61],"consider":[62],"infinite":[64],"$G({\\bf":[66],"Z}^+,":[67],"p)$,":[68],"$p$":[70],"fixed,":[72],"and":[73],"three":[76],"one.":[85],"The":[86],"main":[87],"results":[88],"are":[89],"proved":[90],"using":[91],"second":[93],"moment":[94],"method":[95],"together":[96],"Borel":[99],"Cantelli":[100],"lemma.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}