{"id":"https://openalex.org/W4224278445","doi":"https://doi.org/10.3390/axioms11050191","title":"A Survey on the k-Path Vertex Cover Problem","display_name":"A Survey on the k-Path Vertex Cover Problem","publication_year":2022,"publication_date":"2022-04-20","ids":{"openalex":"https://openalex.org/W4224278445","doi":"https://doi.org/10.3390/axioms11050191"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11050191","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050191","pdf_url":"https://www.mdpi.com/2075-1680/11/5/191/pdf?version=1650514839","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/5/191/pdf?version=1650514839","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101728553","display_name":"Jianhua Tu","orcid":"https://orcid.org/0000-0002-7667-2116"},"institutions":[{"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"]},{"id":"https://openalex.org/I179026463","display_name":"Beijing Technology and Business University","ror":"https://ror.org/013e0zm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I179026463"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianhua Tu","raw_affiliation_strings":["Key Laboratory of Tibetan Information Processing and Machine Translation, Xining 810008, China","Key Laboratory of Tibetan Information Processing, Ministry of Education, Xining 810008, China","School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Tibetan Information Processing and Machine Translation, Xining 810008, China","institution_ids":["https://openalex.org/I4210121080"]},{"raw_affiliation_string":"Key Laboratory of Tibetan Information Processing, Ministry of Education, Xining 810008, China","institution_ids":[]},{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China","institution_ids":["https://openalex.org/I179026463"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101728553"],"corresponding_institution_ids":["https://openalex.org/I179026463","https://openalex.org/I4210121080"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5843,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.68358108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"5","first_page":"191","last_page":"191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9973000288009644,"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/T12288","display_name":"Optimization and Search Problems","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/combinatorics","display_name":"Combinatorics","score":0.7329552173614502},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.6989251971244812},{"id":"https://openalex.org/keywords/edge-cover","display_name":"Edge cover","score":0.6548904180526733},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6338291168212891},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.5756635069847107},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5131273865699768},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49741581082344055},{"id":"https://openalex.org/keywords/distance","display_name":"Distance","score":0.48087719082832336},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41179007291793823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37749046087265015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19832879304885864},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.16201651096343994}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7329552173614502},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.6989251971244812},{"id":"https://openalex.org/C17762858","wikidata":"https://www.wikidata.org/wiki/Q594001","display_name":"Edge cover","level":3,"score":0.6548904180526733},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6338291168212891},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.5756635069847107},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5131273865699768},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49741581082344055},{"id":"https://openalex.org/C54385418","wikidata":"https://www.wikidata.org/wiki/Q2742711","display_name":"Distance","level":4,"score":0.48087719082832336},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41179007291793823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37749046087265015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19832879304885864},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.16201651096343994},{"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":3,"locations":[{"id":"doi:10.3390/axioms11050191","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050191","pdf_url":"https://www.mdpi.com/2075-1680/11/5/191/pdf?version=1650514839","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a2553d7d195c461d9a1ba30b3059549f","is_oa":true,"landing_page_url":"https://doaj.org/article/a2553d7d195c461d9a1ba30b3059549f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 5, p 191 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/5/191/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11050191","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 5; Pages: 191","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11050191","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050191","pdf_url":"https://www.mdpi.com/2075-1680/11/5/191/pdf?version=1650514839","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4224278445.pdf","grobid_xml":"https://content.openalex.org/works/W4224278445.grobid-xml"},"referenced_works_count":78,"referenced_works":["https://openalex.org/W94353364","https://openalex.org/W154393378","https://openalex.org/W880397381","https://openalex.org/W1518653692","https://openalex.org/W1924647272","https://openalex.org/W1968635621","https://openalex.org/W1987064693","https://openalex.org/W1987796300","https://openalex.org/W1990092116","https://openalex.org/W2003830843","https://openalex.org/W2007945292","https://openalex.org/W2012391569","https://openalex.org/W2012931553","https://openalex.org/W2013415302","https://openalex.org/W2014363582","https://openalex.org/W2014981179","https://openalex.org/W2016639462","https://openalex.org/W2034112762","https://openalex.org/W2038294264","https://openalex.org/W2052790720","https://openalex.org/W2053240544","https://openalex.org/W2058258808","https://openalex.org/W2059451253","https://openalex.org/W2061237693","https://openalex.org/W2063292059","https://openalex.org/W2069827532","https://openalex.org/W2070576097","https://openalex.org/W2071170329","https://openalex.org/W2125447390","https://openalex.org/W2125455032","https://openalex.org/W2131265210","https://openalex.org/W2137118456","https://openalex.org/W2137986027","https://openalex.org/W2141925838","https://openalex.org/W2144050783","https://openalex.org/W2179466049","https://openalex.org/W2199703934","https://openalex.org/W2216743162","https://openalex.org/W2218434618","https://openalex.org/W2231757830","https://openalex.org/W2248154729","https://openalex.org/W2264404578","https://openalex.org/W2275951435","https://openalex.org/W2281477993","https://openalex.org/W2401114553","https://openalex.org/W2412257713","https://openalex.org/W2472778302","https://openalex.org/W2552909035","https://openalex.org/W2592808588","https://openalex.org/W2615367498","https://openalex.org/W2792542893","https://openalex.org/W2794671365","https://openalex.org/W2794918889","https://openalex.org/W2795299670","https://openalex.org/W2808514443","https://openalex.org/W2903563585","https://openalex.org/W2910056170","https://openalex.org/W2911678318","https://openalex.org/W2963377146","https://openalex.org/W2963649373","https://openalex.org/W2963995309","https://openalex.org/W2984212031","https://openalex.org/W3014552119","https://openalex.org/W3028203334","https://openalex.org/W3080897928","https://openalex.org/W3113201831","https://openalex.org/W3183859668","https://openalex.org/W3206448149","https://openalex.org/W4205345914","https://openalex.org/W4210756314","https://openalex.org/W4232896595","https://openalex.org/W6603813287","https://openalex.org/W6700437645","https://openalex.org/W6701035701","https://openalex.org/W6738383572","https://openalex.org/W6749437415","https://openalex.org/W6757179248","https://openalex.org/W6758016736"],"related_works":["https://openalex.org/W2949255922","https://openalex.org/W2036594069","https://openalex.org/W4244658307","https://openalex.org/W2156896570","https://openalex.org/W2038655901","https://openalex.org/W1627181101","https://openalex.org/W2043560626","https://openalex.org/W1558145674","https://openalex.org/W4287780535","https://openalex.org/W3021699323"],"abstract_inverted_index":{"Given":[0],"an":[1],"integer":[2],"k":[3,12],"\u2265":[4],"2,":[5],"a":[6,9,19,24,48,82,88,96],"k-path":[7,25,37,42,49,65,73,84,111,117],"is":[8,22,47,62,79],"path":[10],"on":[11],"vertices.":[13],"A":[14,40],"set":[15],"of":[16,35,38,57,69,99,103,109],"vertices":[17,58],"in":[18,45,87,106],"graph":[20],"G":[21,46],"called":[23,63],"vertex":[26,34,43,50,66,74,85,112,118],"cover":[27,44,51,67,75,86,113,119],"if":[28],"it":[29],"includes":[30],"at":[31],"least":[32],"one":[33],"every":[36],"G.":[39,70],"minimum":[41,83],"having":[52],"the":[53,64,72,77,100,104,107,110,116],"smallest":[54],"possible":[55],"number":[56,68],"and":[59,115],"its":[60],"cardinality":[61],"In":[71,91],"problem,":[76],"goal":[78],"to":[80],"find":[81],"given":[89],"graph.":[90],"this":[92],"paper,":[93],"we":[94],"present":[95],"brief":[97],"survey":[98],"current":[101],"state":[102],"art":[105],"study":[108],"problem":[114],"number.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
