Feedback vertex sets and cyclically reducible graphs
Journal of the ACM (JACM)
The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
On locating minimum feedback vertex sets
Journal of Computer and System Sciences
The complexity of generalized clique covering
Discrete Applied Mathematics
On the feedback vertex set problem in permutation graphs
Information Processing Letters
A linear-time algorithm for the weighted feedback vertex problem on interval graphs
Information Processing Letters
Almost exact minimum feedback vertex set in meshes and butterflies
Information Processing Letters
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Solving the feedback vertex set problem on undirected graphs
Discrete Applied Mathematics
Approximating minimum feedback vertex sets in hypergraphs
Theoretical Computer Science
Feedback vertex set in hypercubes
Information Processing Letters
Wavelength conversion in optical networks
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
New bounds on the size of the minimum feedback vertex set in meshes and butterflies
Information Processing Letters
Minimum feedback vertex sets in shuffle-based interconnection networks
Information Processing Letters
Feedback vertex sets in star graphs
Information Processing Letters
Hi-index | 0.90 |
Butterflies are undirected graphs of bounded degree. They are widely used as interconnection networks. In this paper we study the feedback vertex set problem for butterflies. We show that the feedback vertex set found by Luccio's algorithm [Inform. Process. Lett. 66 (1998) 59-64] for the k-dimensional butterfly Bk is of size ⌊(3k + 1)2k + 1/9⌋. Besides, we propose an algorithm to find a feedback vertex set of size either ⌊(3k + 1)2k + 1/9⌋ - 2k - 1/3 or ⌊(3k + 1)2k + 1/9⌋ - 2k - 2 ⌈k/2⌉ - 2⌊k/2⌋ + 1 / 3 for Bk depending on whether k is even or odd.