A Randomized Polynomial Kernel for Subset Feedback Vertex Set
نویسندگان
چکیده
منابع مشابه
A quadratic kernel for feedback vertex set
We prove that given an undirected graph G on n vertices and an integer k, one can compute in polynomial time in n a graph G′ with at most 5k+k vertices and an integer k′ such that G has a feedback vertex set of size at most k iff G′ has a feedback vertex set of size at most k′. This result improves a previous O(k) kernel of Burrage et al. [6], and a more recent cubic kernel of Bodlaender [3]. T...
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In this paper, it is shown that the Feedback Vertex Set problem on unweighted, undirected graphs has a kernel of cubic size. I.e., a polynomial time algorithm is described, that, when given a graph G and an integer k, finds a graph H and integer k′ ≤ k, such that H has a feedback vertex set with at most k′ vertices, if and only if G has a feedback vertex set with at most k vertices, and H has a...
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Given a graph G and a parameter k, the Chordal Vertex Deletion (CVD) problem asks whether there exists a subset U ⊆ V (G) of size at most k that hits all induced cycles of size at least 4. The existence of a polynomial kernel for CVD was a well-known open problem in the field of Parameterized Complexity. Recently, Jansen and Pilipczuk resolved this question affirmatively by designing a polynomi...
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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 کاملSubset Feedback Vertex Set Is Fixed-Parameter Tractable
The classical FEEDBACK VERTEX SET problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. FEEDBACK VERTEX SET has attracted a large amount of research in the parameterized setting, and subsequent kernelization and fixed-parameter algorithms have been a rich source of ideas in the field. In this paper we consider...
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ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2017
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s00224-017-9805-6