{"id":"https://openalex.org/W7166141542","doi":"https://doi.org/10.1016/j.disc.2026.115303","title":"Counterexamples to a problem of Spiro on k-kernels","display_name":"Counterexamples to a problem of Spiro on k-kernels","publication_year":2026,"publication_date":"2026-06-26","ids":{"openalex":"https://openalex.org/W7166141542","doi":"https://doi.org/10.1016/j.disc.2026.115303"},"language":"en","primary_location":{"id":"doi:10.1016/j.disc.2026.115303","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.disc.2026.115303","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/A5138153859","display_name":"\u738b\u6653\u7fca","orcid":null},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyi Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Qinghai Normal University, Xining, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qinghai Normal University, Xining, China","institution_ids":["https://openalex.org/I20616075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139458635","display_name":"Bo Deng","orcid":null},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]},{"id":"https://openalex.org/I4210121080","display_name":"Qinghai Tibetan Hospital","ror":"https://ror.org/03mmka096","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210121080"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Deng","raw_affiliation_strings":["Academy of Plateau Science and Sustainability, Xining, 810016, China","School of Mathematics and Statistics, Qinghai Normal University, Xining, China","The State Key Laboratory of Tibetan Intelligence, Xining, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academy of Plateau Science and Sustainability, Xining, 810016, China","institution_ids":[]},{"raw_affiliation_string":"School of Mathematics and Statistics, Qinghai Normal University, Xining, China","institution_ids":["https://openalex.org/I20616075"]},{"raw_affiliation_string":"The State Key Laboratory of Tibetan Intelligence, Xining, China","institution_ids":["https://openalex.org/I4210121080"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086480850","display_name":"Bin Chen","orcid":"https://orcid.org/0000-0003-2965-0333"},"institutions":[{"id":"https://openalex.org/I4210107712","display_name":"Fujian Business University","ror":"https://ror.org/01mc04w21","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210107712"]},{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]},{"id":"https://openalex.org/I83791580","display_name":"Fujian University of Technology","ror":"https://ror.org/03c8fdb16","country_code":"CN","type":"education","lineage":["https://openalex.org/I83791580"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bin Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Fuzhou University, Fujian, China"],"raw_orcid":"https://orcid.org/0000-0003-2965-0333","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Fuzhou University, Fujian, China","institution_ids":["https://openalex.org/I4210107712","https://openalex.org/I80947539","https://openalex.org/I83791580"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5086480850"],"corresponding_institution_ids":["https://openalex.org/I4210107712","https://openalex.org/I80947539","https://openalex.org/I83791580"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.86566485,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"349","issue":"12","first_page":"115303","last_page":"115303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10884","display_name":"Holomorphic and Operator Theory","score":0.15279999375343323,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.15279999375343323,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.08290000259876251,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12351","display_name":"Geometry and complex manifolds","score":0.065700002014637,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.9617000222206116},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.8424000144004822},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6888999938964844},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.423799991607666},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.38749998807907104},{"id":"https://openalex.org/keywords/strongly-connected-component","display_name":"Strongly connected component","score":0.33500000834465027}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.9617000222206116},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8515999913215637},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.8424000144004822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8331000208854675},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6888999938964844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5084999799728394},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C38754835","wikidata":"https://www.wikidata.org/wiki/Q2003238","display_name":"Strongly connected component","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C136134351","wikidata":"https://www.wikidata.org/wiki/Q431937","display_name":"Antichain","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.273499995470047}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.disc.2026.115303","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.disc.2026.115303","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":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W4248423866","https://openalex.org/W4362580985","https://openalex.org/W4403927754","https://openalex.org/W7116372806"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-28T06:15:30.350997","created_date":"2026-06-27T00:00:00"}
