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New bounds on the size of the minimum feedback vertex set in meshes and butterflies

✍ Scribed by Ioannis Caragiannis; Christos Kaklamanis; Panagiotis Kanellopoulos

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
113 KB
Volume
83
Category
Article
ISSN
0020-0190

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In this paper a new upper bound for the feedback set of cubic graphs is obtained. This result answers a question posed by Speckenmeyer (1986, 1988) in the field of feedback vertex set and improves several former results due to Bondy et al. (1987). Also this new bound is sharp in some cases.

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Let D = {B1 , B2 , . . . , B b } be a finite family of k-subsets (called blocks) of a vset X(v) = {1, 2, . . . , v} (with elements called points). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks, b, is the size