{"id":"https://openalex.org/W1509731218","doi":"https://doi.org/10.1007/978-3-642-02026-1_24","title":"A Sufficient and Necessary Condition for the Forcing Number of a Bipartite Graph Being Equal to the Minimum Number of Trailing Vertices","display_name":"A Sufficient and Necessary Condition for the Forcing Number of a Bipartite Graph Being Equal to the Minimum Number of Trailing Vertices","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1509731218","doi":"https://doi.org/10.1007/978-3-642-02026-1_24","mag":"1509731218"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-02026-1_24","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-02026-1_24","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5052781227","display_name":"Hongwei Wang","orcid":"https://orcid.org/0000-0001-9393-2701"},"institutions":[{"id":"https://openalex.org/I15823474","display_name":"Linyi University","ror":"https://ror.org/01knv0402","country_code":"CN","type":"education","lineage":["https://openalex.org/I15823474"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongwei Wang","raw_affiliation_strings":["Department of Mathematics, Linyi Normal University, Linyi, Shandong, 276005, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Linyi Normal University, Linyi, Shandong, 276005, China","institution_ids":["https://openalex.org/I15823474"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052781227"],"corresponding_institution_ids":["https://openalex.org/I15823474"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.0055,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.84443099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"258","last_page":"268"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9991000294685364,"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":0.9991000294685364,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9984999895095825,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8842800855636597},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6720900535583496},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6190735101699829},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5417921543121338},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5211563110351562},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5192551612854004},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.49116942286491394},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.45005935430526733},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4464167058467865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4207620620727539},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.043774932622909546}],"concepts":[{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8842800855636597},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6720900535583496},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6190735101699829},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5417921543121338},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5211563110351562},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5192551612854004},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.49116942286491394},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.45005935430526733},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4464167058467865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4207620620727539},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.043774932622909546},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-02026-1_24","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-02026-1_24","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.550000011920929,"display_name":"Climate action"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323252","display_name":"Linyi University","ror":"https://ror.org/01knv0402"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W96016000","https://openalex.org/W1986535470","https://openalex.org/W1988825590","https://openalex.org/W1991113119","https://openalex.org/W1999789113","https://openalex.org/W2005851739","https://openalex.org/W2035531039","https://openalex.org/W2053217301","https://openalex.org/W2053934832","https://openalex.org/W2063528026","https://openalex.org/W2071588921","https://openalex.org/W2073463908","https://openalex.org/W2084737762","https://openalex.org/W2087090178","https://openalex.org/W2128803626","https://openalex.org/W2145865477","https://openalex.org/W2155190380","https://openalex.org/W2309179828","https://openalex.org/W2348808260","https://openalex.org/W2611093227","https://openalex.org/W2964089109","https://openalex.org/W3043060850","https://openalex.org/W3158297100","https://openalex.org/W4232896595","https://openalex.org/W4249367555"],"related_works":["https://openalex.org/W2174899211","https://openalex.org/W2091826982","https://openalex.org/W4400909662","https://openalex.org/W2921162226","https://openalex.org/W2036057584","https://openalex.org/W3022526073","https://openalex.org/W4246000090","https://openalex.org/W2107875203","https://openalex.org/W4234658180","https://openalex.org/W3098480989"],"abstract_inverted_index":null,"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}