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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/15856

Title: Complexity of the Maximum k-Path Vertex Cover Problem
Authors: Miyano, Eiji
Saitoh, Toshiki
Uehara, Ryuhei
Yagita, Tsuyoshi
Zanden, Tom van der
Keywords: path vertex cover problem
split graph
Issue Date: 2018-01-31
Publisher: Springer
Magazine name: Lecture Notes in Computer Science
Volume: 10755
Start page: 240
End page: 251
DOI: 10.1007/978-3-319-75172-6_21
Abstract: This paper introduces the maximum version of the k-path vertex cover problem, called the Maximum k-Path Vertex Cover problem (MaxP_k VC for short): A path consisting of k vertices, i.e., a path of length k-1 is called a k-path. If a k-path P_k includes a vertex v in a vertex set S, then we say that S or v covers Pk . Given a graph G=(V,E) and an integer s, the goal of MaxP_kVC is to find a vertex subset S included in V of at most s vertices such that the number of k-paths covered by S is maximized. MaxPk VC is generally NP-hard. In this paper we consider the tractability/intractability of MaxP_kVC on subclasses of graphs: We prove that MaxP_3 VC and MaxP_4VC remain NP-hard even for split graphs and for chordal graphs, respectively. Furthermore, if the input graph is restricted to graphs with constant bounded treewidth, then MaxP_3 VC can be solved in polynomial time.
Rights: This is the author-created version of Springer, Eiji Miyano, Toshiki Saitoh, Ryuhei Uehara, Tsuyoshi Yagita and Tom van der Zanden, Lecture Notes in Computer Science, 10755, 2018, 240-251. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/978-3-319-75172-6_21
URI: http://hdl.handle.net/10119/15856
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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