Given an undirected and vertex weighted graph G, the Weighted Feedback Vertex Problem (WFVP) consists in finding a subset F ⊆ V of vertices of minimum weight such that each cycle in G contains at least one vertex in F. The WFVP on general graphs is known to be NP-hard. In this paper we introduce a new class of graphs, namely the diamond graphs, and give a linear time algorithm to solve WFVP on it.

A linear time algorithm for the minimum Weighted Feedback Vertex Set on diamonds

CARRABS, FRANCESCO;CERULLI, Raffaele;GENTILI, Monica;
2005-01-01

Abstract

Given an undirected and vertex weighted graph G, the Weighted Feedback Vertex Problem (WFVP) consists in finding a subset F ⊆ V of vertices of minimum weight such that each cycle in G contains at least one vertex in F. The WFVP on general graphs is known to be NP-hard. In this paper we introduce a new class of graphs, namely the diamond graphs, and give a linear time algorithm to solve WFVP on it.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/2501735
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