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doi:10.1016/j.ipl.2004.03.005 
Copyright © 2004 Elsevier B.V. All rights reserved.
New upper bounds on feedback vertex numbers in butterflies*1
Received 4 September 2003;
Revised 1 March 2004.
Communicated by Wen-Lian Hsu
Available online 9 April 2004.
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Abstract
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
. Besides, we propose an algorithm to find a feedback vertex set of size either
or
for Bk depending on whether k is even or odd.
Author Keywords: Interconnection networks; Butterfly; Feedback vertex sets
