{"id":"https://openalex.org/W4210755957","doi":"https://doi.org/10.1016/s0012-365x(99)90107-3","title":"Polarities and 2k-cycle-free graphs","display_name":"Polarities and 2k-cycle-free graphs","publication_year":1999,"publication_date":"1999-02-01","ids":{"openalex":"https://openalex.org/W4210755957","doi":"https://doi.org/10.1016/s0012-365x(99)90107-3"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(99)90107-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)90107-3","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/A5031529103","display_name":"Felix Lazebnik","orcid":null},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Felix Lazebnik","raw_affiliation_strings":["Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113014824","display_name":"V. A. Ustimenko","orcid":null},"institutions":[{"id":"https://openalex.org/I189238007","display_name":"Taras Shevchenko National University of Kyiv","ror":"https://ror.org/02aaqv166","country_code":"UA","type":"education","lineage":["https://openalex.org/I189238007"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Vasiliy A. Ustimenko","raw_affiliation_strings":["Department of Mathematics and Mechanics, University of Kiev, Kiev 252127, Ukraine"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mechanics, University of Kiev, Kiev 252127, Ukraine","institution_ids":["https://openalex.org/I189238007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043002667","display_name":"Andrew J. Woldar","orcid":"https://orcid.org/0000-0002-5678-8648"},"institutions":[{"id":"https://openalex.org/I7863295","display_name":"Villanova University","ror":"https://ror.org/02g7kd627","country_code":"US","type":"education","lineage":["https://openalex.org/I7863295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew J. Woldar","raw_affiliation_strings":["Department of Mathematical Sciences, Villanova University, Villanova, PA 19085, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Villanova University, Villanova, PA 19085, USA","institution_ids":["https://openalex.org/I7863295"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031529103"],"corresponding_institution_ids":["https://openalex.org/I86501945"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.35220126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"197-198","issue":null,"first_page":"503","last_page":"513"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","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/T11476","display_name":"Graph theory and applications","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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9986000061035156,"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":0.849565863609314},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8446396589279175},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5344352722167969},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5243606567382812},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5207272171974182},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5024209022521973},{"id":"https://openalex.org/keywords/induced-subgraph","display_name":"Induced subgraph","score":0.4952372610569},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4599081873893738},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.44932374358177185},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06689494848251343}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.849565863609314},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8446396589279175},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5344352722167969},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5243606567382812},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5207272171974182},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5024209022521973},{"id":"https://openalex.org/C2778012994","wikidata":"https://www.wikidata.org/wiki/Q24743362","display_name":"Induced subgraph","level":4,"score":0.4952372610569},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4599081873893738},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.44932374358177185},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06689494848251343},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"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:10.1016/s0012-365x(99)90107-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)90107-3","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W71326099","https://openalex.org/W151791740","https://openalex.org/W180459414","https://openalex.org/W181128013","https://openalex.org/W1607979118","https://openalex.org/W1987996179","https://openalex.org/W1991809067","https://openalex.org/W1999534475","https://openalex.org/W2003132645","https://openalex.org/W2009852526","https://openalex.org/W2012280556","https://openalex.org/W2021022635","https://openalex.org/W2035971565","https://openalex.org/W2040040623","https://openalex.org/W2040452405","https://openalex.org/W2082538734","https://openalex.org/W2087806988","https://openalex.org/W2093219044","https://openalex.org/W2110805362","https://openalex.org/W6636374305","https://openalex.org/W6723928287"],"related_works":["https://openalex.org/W2152992791","https://openalex.org/W2112835755","https://openalex.org/W2349674371","https://openalex.org/W2963262648","https://openalex.org/W2097495471","https://openalex.org/W2025239573","https://openalex.org/W2158905189","https://openalex.org/W4319874546","https://openalex.org/W1157790564","https://openalex.org/W3051524360"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}