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A minimum k-path vertex cover in G is a k-path vertex cover having the smallest possible number of vertices and its cardinality is called the k-path vertex cover number of G. In the k-path vertex cover problem, the goal is to find a minimum k-path vertex cover in a given graph. In this paper, we present a brief survey of the current state of the art in the study of the k-path vertex cover problem and the k-path vertex cover number.<\/jats:p>","DOI":"10.3390\/axioms11050191","type":"journal-article","created":{"date-parts":[[2022,4,21]],"date-time":"2022-04-21T01:55:51Z","timestamp":1650506151000},"page":"191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Survey on the k-Path Vertex Cover Problem"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7667-2116","authenticated-orcid":false,"given":"Jianhua","family":"Tu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China"},{"name":"Key Laboratory of Tibetan Information Processing and Machine Translation, Xining 810008, China"},{"name":"Key Laboratory of Tibetan Information Processing, Ministry of Education, Xining 810008, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bondy, J.A., and Murty, U.S.R. 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