{"id":"https://openalex.org/W2022743540","doi":"https://doi.org/10.1016/0012-365x(78)90147-4","title":"Covering the vertex set of a graph with subgraphs of smaller degree","display_name":"Covering the vertex set of a graph with subgraphs of smaller degree","publication_year":1978,"publication_date":"1978-01-01","ids":{"openalex":"https://openalex.org/W2022743540","doi":"https://doi.org/10.1016/0012-365x(78)90147-4","mag":"2022743540"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(78)90147-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(78)90147-4","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/A5058170476","display_name":"Jim Lawrence","orcid":"https://orcid.org/0000-0003-0638-2559"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jim Lawrence","raw_affiliation_strings":["Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas at Austin, Austin, TX 78712, U.S.A","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058170476"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":1.5749,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.83282675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"1","first_page":"61","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9966999888420105,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9966999888420105,"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":0.9941999912261963,"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":0.991100013256073,"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/combinatorics","display_name":"Combinatorics","score":0.8739414215087891},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8017885684967041},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5417211651802063},{"id":"https://openalex.org/keywords/windmill-graph","display_name":"Windmill graph","score":0.47777116298675537},{"id":"https://openalex.org/keywords/regular-graph","display_name":"Regular graph","score":0.46358180046081543},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.4580269455909729},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.45566123723983765},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.43464523553848267},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"Graph factorization","score":0.4328596889972687},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.42619356513023376},{"id":"https://openalex.org/keywords/wheel-graph","display_name":"Wheel graph","score":0.42593562602996826},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.42519354820251465},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4034353494644165},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.30775102972984314}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8739414215087891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8017885684967041},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5417211651802063},{"id":"https://openalex.org/C73380178","wikidata":"https://www.wikidata.org/wiki/Q8024306","display_name":"Windmill graph","level":5,"score":0.47777116298675537},{"id":"https://openalex.org/C123482549","wikidata":"https://www.wikidata.org/wiki/Q826467","display_name":"Regular graph","level":5,"score":0.46358180046081543},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.4580269455909729},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.45566123723983765},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.43464523553848267},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.4328596889972687},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.42619356513023376},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.42593562602996826},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.42519354820251465},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4034353494644165},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.30775102972984314},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(78)90147-4","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(78)90147-4","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1530753374","https://openalex.org/W1552744309","https://openalex.org/W2085716675","https://openalex.org/W2146982094","https://openalex.org/W2313449717","https://openalex.org/W2313512971","https://openalex.org/W2577446513","https://openalex.org/W2588591072","https://openalex.org/W4236466742","https://openalex.org/W6682002315"],"related_works":["https://openalex.org/W4298388358","https://openalex.org/W3209447868","https://openalex.org/W1989256506","https://openalex.org/W2185981630","https://openalex.org/W2391570583","https://openalex.org/W2161439427","https://openalex.org/W2792739039","https://openalex.org/W2063965319","https://openalex.org/W4311409474","https://openalex.org/W4388319796"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"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":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
