A Cubic Kernel for Feedback Vertex Set and Loop Cutset
نویسندگان
چکیده
منابع مشابه
A Cubic Kernel for Feedback Vertex Set
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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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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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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ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2009
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s00224-009-9234-2