On the nonseparating independent set problem and feedback set problem for graphs with no vertex degree exceeding three
نویسندگان
چکیده
منابع مشابه
Solving the feedback vertex set problem on undirected graphs
Feedback problems consist of removing a minimal number of vertices of a directed or undirected graph in order to make it acyclic. The problem is known to be NPcomplete. In this paper we consider the variant on undirected graphs. The polyhedral structure of the Feedback Vertex Set polytope is studied. We prove that this polytope is full dimensional and show that some inequalities are facet de ni...
متن کاملDeterministic Algorithms for the Independent Feedback Vertex Set Problem
A feedback vertex set F of an undirected graph G is a vertex subset of G whose removal results in a forest. Such a set F is said to be independent if F forms an independent set of G. In this paper, we study the problem of finding an independent feedback vertex set of a given graph with the minimum number of vertices, from the viewpoint of graph classes. This problem is NP-hard even for planar b...
متن کاملPolynomial-Time Algorithms for the Subset Feedback Vertex Set Problem on Interval Graphs and Permutation Graphs
Given a vertex-weighted graph G = (V,E) and a set S ⊆ V , a subset feedback vertex set X is a set of the vertices of G such that the graph induced by V \ X has no cycle containing a vertex of S. The Subset Feedback Vertex Set problem takes as input G and S and asks for the subset feedback vertex set of minimum total weight. In contrast to the classical Feedback Vertex Set problem which is obtai...
متن کاملDirected Feedback Vertex Set Problem is FPT
To decide if the parameterized feedback vertex set problem in directed graph is fixed-parameter tractable is a long time open problem. In this paper, we prove that the parameterized feedback vertex set in directed graph is fixed-parameter tractable and give the first FPT algorithm of running time O((1.48k)n) for it. As the feedback arc set problem in directed graph can be transformed to a feedb...
متن کاملIndependent Feedback Vertex Set for P_5-free Graphs
The NP-complete problem Feedback Vertex Set is that of deciding whether or not it is possible, for a given integer k ≥ 0, to delete at most k vertices from a given graph so that what remains is a forest. The variant in which the deleted vertices must form an independent set is called Independent Feedback Vertex Set and is also NP-complete. In fact, even deciding if an independent feedback verte...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1988
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90226-9