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 Tr. Inst. Mat., 2017, Volume 25, Number 1, Pages 62–81 (Mi timb269)

The weighted $k$-path vertex cover problem on series-parallel graphs

V. V. Lepin

Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract: Given a graph $G$ with a vertex weight function $\omega_V: V(G)\to\mathbb{R}^+$ and a positive integer $k,$ we consider the weighted $k$-path vertex cover problem: it consists in finding a minimum-weight subset $S$ of vertices of a graph $G$ such that every path of order $k$ in $G$ contains at least one vertex from $S.$ We give $O(n)$ algorithms for finding the minimum weight of $k$-path vertex cover and connected $k$-path vertex cover for series-parallel graphs.

 Funding Agency Grant Number Belarusian Republican Foundation for Fundamental Research Ô16ÐÀ-003

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UDC: 519.1

Citation: V. V. Lepin, “The weighted $k$-path vertex cover problem on series-parallel graphs”, Tr. Inst. Mat., 25:1 (2017), 62–81

Citation in format AMSBIB
\Bibitem{Lep17}
\by V.~V.~Lepin
\paper The weighted $k$-path vertex cover problem on series-parallel graphs
\jour Tr. Inst. Mat.
\yr 2017
\vol 25
\issue 1
\pages 62--81
\mathnet{http://mi.mathnet.ru/timb269}