{"id":"https://openalex.org/W2027384327","doi":"https://doi.org/10.1017/s0963548305007431","title":"On the Independent Domination Number of Random Regular Graphs","display_name":"On the Independent Domination Number of Random Regular Graphs","publication_year":2006,"publication_date":"2006-06-07","ids":{"openalex":"https://openalex.org/W2027384327","doi":"https://doi.org/10.1017/s0963548305007431","mag":"2027384327"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548305007431","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548305007431","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009575159","display_name":"William Duckworth","orcid":null},"institutions":[{"id":"https://openalex.org/I99043593","display_name":"Macquarie University","ror":"https://ror.org/01sf06y89","country_code":"AU","type":"education","lineage":["https://openalex.org/I99043593"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"W. DUCKWORTH","raw_affiliation_strings":["Department of Computing, Macquarie University Sydney, NSW 2109, Australia (e-mail:","Department of Computing, Macquarie University Sydney, NSW 2109, Australia (e-mail: billy@ics.mq.edu.au)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computing, Macquarie University Sydney, NSW 2109, Australia (e-mail:","institution_ids":["https://openalex.org/I99043593"]},{"raw_affiliation_string":"Department of Computing, Macquarie University Sydney, NSW 2109, Australia (e-mail: billy@ics.mq.edu.au)","institution_ids":["https://openalex.org/I99043593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114010170","display_name":"N. C. 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":"N. C. WORMALD","raw_affiliation_strings":["Department of Combinatorics & Optimization University of Waterloo, Waterloo ON, Canada N2L 3G1 (e-mail:","Department of Combinatorics & Optimization University of Waterloo, Waterloo ON, Canada N2L 3G1 (e-mail: nickwor@math.uwaterloo.ca)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Combinatorics & Optimization University of Waterloo, Waterloo ON, Canada N2L 3G1 (e-mail:","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics & Optimization University of Waterloo, Waterloo ON, Canada N2L 3G1 (e-mail: nickwor@math.uwaterloo.ca)","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6619,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.89573204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"4","first_page":"513","last_page":"522"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994000196456909,"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":0.9948999881744385,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7400853633880615},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.6251914501190186},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.611819863319397},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6073812246322632},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5496687293052673},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.5494916439056396},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4740676283836365},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.4723195731639862},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4635412395000458},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4317692518234253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20631879568099976},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.20077228546142578},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.16865107417106628},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.10524016618728638}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7400853633880615},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.6251914501190186},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.611819863319397},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6073812246322632},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5496687293052673},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.5494916439056396},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4740676283836365},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.4723195731639862},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4635412395000458},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4317692518234253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20631879568099976},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.20077228546142578},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.16865107417106628},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.10524016618728638},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548305007431","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548305007431","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W5090298","https://openalex.org/W1497149493","https://openalex.org/W1591536422","https://openalex.org/W1592213313","https://openalex.org/W1976422444","https://openalex.org/W1979720612","https://openalex.org/W2003159902","https://openalex.org/W2008704324","https://openalex.org/W2037318072","https://openalex.org/W2038225707","https://openalex.org/W2040924621","https://openalex.org/W2094803507","https://openalex.org/W2798588639","https://openalex.org/W2905110430","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W300018836","https://openalex.org/W2029336174","https://openalex.org/W2031662678","https://openalex.org/W3037291746","https://openalex.org/W2971872036","https://openalex.org/W3164644441","https://openalex.org/W2906881967","https://openalex.org/W2935770235","https://openalex.org/W2736530170","https://openalex.org/W3178466616"],"abstract_inverted_index":{"A":[0],"dominating":[1],"set":[2],".":[3],"In":[4],"this":[5],"paper":[6],"we":[7],"present":[8],"upper":[9],"bounds":[10],"on":[11,32],"the":[12,25],"independent":[13],"domination":[14],"number":[15],"of":[16,27],"random":[17,33],"regular":[18,34],"graphs.":[19],"This":[20],"is":[21],"achieved":[22],"by":[23],"analysing":[24],"performance":[26],"a":[28],"randomized":[29],"greedy":[30],"algorithm":[31],"graphs":[35],"using":[36],"differential":[37],"equations.":[38]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}