{"id":"https://openalex.org/W1491127810","doi":"https://doi.org/10.4086/toc.2011.v007a003","title":"","display_name":"","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1491127810","doi":"https://doi.org/10.4086/toc.2011.v007a003","mag":"1491127810"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2011.v007a003","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a003","pdf_url":"https://theoryofcomputing.org/articles/v007a003/v007a003.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v007a003/v007a003.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055776088","display_name":"Per Austrin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Per Austrin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067917669","display_name":"Subhash Khot","orcid":"https://orcid.org/0009-0007-9246-4011"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Subhash Khot","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007318528","display_name":"Muli Safra","orcid":"https://orcid.org/0000-0002-5022-7727"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muli Safra","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055776088"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.4627,"has_fulltext":true,"cited_by_count":55,"citation_normalized_percentile":{"value":0.97029884,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"1","first_page":"27","last_page":"43"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9825000166893005,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9682000279426575,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7487316131591797},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.7153484225273132},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6699804067611694},{"id":"https://openalex.org/keywords/hardness-of-approximation","display_name":"Hardness of approximation","score":0.5956004858016968},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5631332397460938},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5132172107696533},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.5034849047660828},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5012903213500977},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.46966302394866943},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45039504766464233},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4312765598297119},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.32631945610046387},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2729725241661072},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1337115466594696},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09553214907646179}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7487316131591797},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.7153484225273132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6699804067611694},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.5956004858016968},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5631332397460938},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5132172107696533},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.5034849047660828},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5012903213500977},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.46966302394866943},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45039504766464233},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4312765598297119},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.32631945610046387},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2729725241661072},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1337115466594696},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09553214907646179},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2011.v007a003","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a003","pdf_url":"https://theoryofcomputing.org/articles/v007a003/v007a003.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2011.v007a003","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2011.v007a003","pdf_url":"https://theoryofcomputing.org/articles/v007a003/v007a003.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1171700966","display_name":null,"funder_award_id":"NSF CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","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/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320322509","display_name":"Kungliga Tekniska H\u00f6gskolan","ror":"https://ror.org/026vcq606"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1491127810.pdf","grobid_xml":"https://content.openalex.org/works/W1491127810.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1483324665","https://openalex.org/W1514622459","https://openalex.org/W1519655831","https://openalex.org/W1859357731","https://openalex.org/W1971749164","https://openalex.org/W1975810219","https://openalex.org/W2014086530","https://openalex.org/W2047861934","https://openalex.org/W2074465184","https://openalex.org/W2078929687","https://openalex.org/W2081254453","https://openalex.org/W2087038607","https://openalex.org/W2091921997","https://openalex.org/W2103649698","https://openalex.org/W2120358419","https://openalex.org/W2125240990","https://openalex.org/W2137118456","https://openalex.org/W2143698439","https://openalex.org/W2152490496","https://openalex.org/W2162117620","https://openalex.org/W2940595899","https://openalex.org/W3140748815","https://openalex.org/W4205765703","https://openalex.org/W4391285994"],"related_works":["https://openalex.org/W2056597184","https://openalex.org/W2359923140","https://openalex.org/W1712180277","https://openalex.org/W2963411648","https://openalex.org/W3184115741","https://openalex.org/W2073435288","https://openalex.org/W2096382750","https://openalex.org/W2952838392","https://openalex.org/W2782292024","https://openalex.org/W1980842804"],"abstract_inverted_index":{"We":[0,13],"study":[1],"the":[2],"inapproximability":[3],"of":[4],"Vertex":[5],"Cover":[6],"and":[7],"Independent":[8],"Set":[9],"on":[10],"degree-d":[11],"graphs.":[12],"prove":[14],"that:":[15]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
