Minimum k-path vertex cover

Abstract : A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by P_k(G) the minimum cardinality of a k-path vertex cover in G. It is shown that the problem of determining P_k(G) is NP-hard for each k ≥ 2, while for trees the problem can be solved in linear time. We investigate upper bounds on the value of P_k(G) and provide several estimations and exact values of P_k(G). We also prove that P_3(G) ≤ (2n + m)/6, for every graph G with n vertices and m edges.
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Submitted on : Thursday, November 10, 2011 - 9:39:20 AM
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Boštjan Brešar, František Kardoš, Ján Katrenič, Gabriel Semanišin. Minimum k-path vertex cover. Discrete Applied Mathematics, Elsevier, 2011, 159 (12), pp.1189-1195. ⟨10.1016/j.dam.2011.04.008⟩. ⟨inria-00634981⟩

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