{"id":"https://openalex.org/W2030384814","doi":"https://doi.org/10.1016/0012-365x(94)00187-n","title":"The vapnik-chervonenkis dimension of a random graph","display_name":"The vapnik-chervonenkis dimension of a random graph","publication_year":1995,"publication_date":"1995-03-01","ids":{"openalex":"https://openalex.org/W2030384814","doi":"https://doi.org/10.1016/0012-365x(94)00187-n","mag":"2030384814"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(94)00187-n","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(94)00187-n","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","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/A5027567103","display_name":"Martin Anthony","orcid":"https://orcid.org/0000-0002-7796-6044"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Martin Anthony","raw_affiliation_strings":["Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039259953","display_name":"Graham Brightwell","orcid":"https://orcid.org/0000-0001-5955-3628"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Graham Brightwell","raw_affiliation_strings":["Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022238950","display_name":"Colin Cooper","orcid":"https://orcid.org/0000-0002-5264-4401"},"institutions":[{"id":"https://openalex.org/I126193024","display_name":"London Metropolitan University","ror":"https://ror.org/00ae33288","country_code":"GB","type":"education","lineage":["https://openalex.org/I126193024"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Colin Cooper","raw_affiliation_strings":["School of Mathematical Studies, University of North London, 2-16 Eden Grove, London N7 8EA, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Studies, University of North London, 2-16 Eden Grove, London N7 8EA, UK","institution_ids":["https://openalex.org/I126193024"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.5272,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.64578665,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"138","issue":"1-3","first_page":"43","last_page":"56"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9976999759674072,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9976999759674072,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9937000274658203,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9900000095367432,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8369361162185669},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6150997877120972},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5397111177444458},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.531658411026001},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48927852511405945},{"id":"https://openalex.org/keywords/vc-dimension","display_name":"VC dimension","score":0.461495965719223}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8369361162185669},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6150997877120972},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5397111177444458},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.531658411026001},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48927852511405945},{"id":"https://openalex.org/C119322782","wikidata":"https://www.wikidata.org/wiki/Q2662236","display_name":"VC dimension","level":2,"score":0.461495965719223}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0012-365x(94)00187-n","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(94)00187-n","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.65.3653","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.65.3653","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.lse.ac.uk/Personal/martin/vcdim.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1530699444","https://openalex.org/W1546328101","https://openalex.org/W1974820192","https://openalex.org/W1995889896","https://openalex.org/W2010029425","https://openalex.org/W2029538739","https://openalex.org/W2054459484","https://openalex.org/W2068871408","https://openalex.org/W2107025376","https://openalex.org/W2154952480","https://openalex.org/W2905110430","https://openalex.org/W4238284510","https://openalex.org/W4292025355","https://openalex.org/W6649323861"],"related_works":["https://openalex.org/W1494863055","https://openalex.org/W2153687934","https://openalex.org/W578536148","https://openalex.org/W2399748593","https://openalex.org/W1608010788","https://openalex.org/W2608720870","https://openalex.org/W2122563501","https://openalex.org/W2902611420","https://openalex.org/W2963241012","https://openalex.org/W4303648909"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}