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Title:  Complexity of the Maximum kPath Vertex Cover Problem 
Authors:  Miyano, Eiji Saitoh, Toshiki Uehara, Ryuhei Yagita, Tsuyoshi Zanden, Tom van der 
Keywords:  path vertex cover problem NPhardness split graph treewidth 
Issue Date:  20180131 
Publisher:  Springer 
Magazine name:  Lecture Notes in Computer Science 
Volume:  10755 
Start page:  240 
End page:  251 
DOI:  10.1007/9783319751726_21 
Abstract:  This paper introduces the maximum version of the kpath vertex cover problem, called the Maximum kPath 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 kpath. If a kpath 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 kpaths covered by S is maximized. MaxPk VC is generally NPhard. 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 NPhard 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 authorcreated version of Springer, Eiji Miyano, Toshiki Saitoh, Ryuhei Uehara, Tsuyoshi Yagita and Tom van der Zanden, Lecture Notes in Computer Science, 10755, 2018, 240251. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/9783319751726_21 
URI:  http://hdl.handle.net/10119/15856 
Material Type:  author 
Appears in Collections:  b101. 雑誌掲載論文 (Journal Articles)

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