Outerplanar obstructions for a feedback vertex set
نویسندگان
چکیده
منابع مشابه
Outerplanar obstructions for a feedback vertex set
For k ≥ 1, letFk be the class of graphs that contain k verticesmeeting all its cycles. Theminor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graphs that do not belong to Fk. We denote by Yk the set of all outerplanar graphs in obs(Fk). In this paper, we provide a precise characterization of the class Yk. Then, using singularity analysis over the counting series obtaine...
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For k ≥ 1, let Fk be the class containing every graph that contains k vertices meeting all its cycles. The minor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graph that does not belong to Fk. We denote by Yk the set of all outerplanar graphs in obs(Fk). In this paper, we provide a precise characterization of the class Yk. Then, using the symbolic method, we prove that ...
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For k ≥ 1, let Fk be the class of graphs that contains k vertices meeting all its cycles. The minor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graph that does not belong to Fk. We denote by Yk the set of all outerplanar graphs in obs(Fk). In this paper, we provide a precise characterization of the class Yk. Then, using singularity analysis over the counting series ob...
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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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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.09.018