{"id":"https://openalex.org/W2048217665","doi":"https://doi.org/10.1007/bf01788692","title":"On directed graphs with an independent covering set","display_name":"On directed graphs with an independent covering set","publication_year":1989,"publication_date":"1989-12-01","ids":{"openalex":"https://openalex.org/W2048217665","doi":"https://doi.org/10.1007/bf01788692","mag":"2048217665"},"language":"en","primary_location":{"id":"doi:10.1007/bf01788692","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01788692","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","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/A5061566251","display_name":"E. C. Milner","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"E. C. Milner","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Calgary, 2500 University Drive, T2N 1N4, Calgary, Alberta, Canada","Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Calgary, 2500 University Drive, T2N 1N4, Calgary, Alberta, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087039640","display_name":"Robert Woodrow","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Robert E. Woodrow","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Calgary, 2500 University Drive, T2N 1N4, Calgary, Alberta, Canada","Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Calgary, 2500 University Drive, T2N 1N4, Calgary, Alberta, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Calgary, Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061566251"],"corresponding_institution_ids":["https://openalex.org/I168635309"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.18470197,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"5","issue":"1","first_page":"363","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","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":0.9966999888420105,"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":0.8333628177642822},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8199490904808044},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.5788518190383911},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.5577775239944458},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5511738657951355},{"id":"https://openalex.org/keywords/feedback-arc-set","display_name":"Feedback arc set","score":0.5090834498405457},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5003714561462402},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.4568328559398651},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3764972984790802},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.19680255651474},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.14530283212661743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8333628177642822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8199490904808044},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.5788518190383911},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.5577775239944458},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5511738657951355},{"id":"https://openalex.org/C157951044","wikidata":"https://www.wikidata.org/wiki/Q1400910","display_name":"Feedback arc set","level":5,"score":0.5090834498405457},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5003714561462402},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.4568328559398651},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3764972984790802},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.19680255651474},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.14530283212661743}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01788692","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01788692","pdf_url":null,"source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W198124755","https://openalex.org/W1482143660","https://openalex.org/W2041481105","https://openalex.org/W2048993351","https://openalex.org/W2144846366","https://openalex.org/W2313512971","https://openalex.org/W4299415759"],"related_works":["https://openalex.org/W1719252778","https://openalex.org/W79682516","https://openalex.org/W2031098440","https://openalex.org/W4307385446","https://openalex.org/W4386875525","https://openalex.org/W2466894780","https://openalex.org/W3092119098","https://openalex.org/W2408522610","https://openalex.org/W3173705736","https://openalex.org/W4286984550"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}