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Minimum feedback vertex sets in shufflebased interconnection networks
 Inform. Process. Lett
, 2003
"... Given a graph G, the problem is to construct a smallest subset S of vertices whose deletion results in an acyclic subgraph. The set S is called a minimum feedback vertex set for G. Tight upper and lower bounds on the cardinality of minimum feedback vertex sets have been obtained for some hypercube–l ..."
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Given a graph G, the problem is to construct a smallest subset S of vertices whose deletion results in an acyclic subgraph. The set S is called a minimum feedback vertex set for G. Tight upper and lower bounds on the cardinality of minimum feedback vertex sets have been obtained for some hypercube–like networks, such as meshes, tori, butterflies, cubeconnected cycles and hypercubes. In this paper we construct minimum feedback vertex sets and determine their cardinalities in certain shufflebased interconnection networks, such as shuffleexchange, de Bruijn and Kautz networks.
Bounds for Minimum Feedback Vertex Sets in Distance Graphs and Circulant Graphs
"... For a set D ⊂ Zn, the distance graph Pn(D) has Zn as its vertex set and the edges are between vertices i and j with i − j  ∈ D. The circulant graph Cn(D) is defined analogously by considering operations modulo n. The minimum feedback vertex set problem consists in finding the smallest number of v ..."
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For a set D ⊂ Zn, the distance graph Pn(D) has Zn as its vertex set and the edges are between vertices i and j with i − j  ∈ D. The circulant graph Cn(D) is defined analogously by considering operations modulo n. The minimum feedback vertex set problem consists in finding the smallest number of vertices to be removed in order to cut all cycles in the graph. This paper studies the minimum feedback vertex set problem for some families of distance graphs and circulant graphs depending on the value of D.
Barcelona Aarhus Barcelona
, 2002
"... This is the second annual progress report for the ALCOMFT project, supported by the European ..."
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This is the second annual progress report for the ALCOMFT project, supported by the European
Feedback numbers of Kautz undirected graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 52 (2012), PAGES 3–9
, 2012
"... The feedback number f(d, n) of the Kautz undirected graph UK(d, n) is the minimum number of vertices whose removal results in an acyclic graph. This paper shows ⌈(dn+1 − dn−1 − 1d(d +1)+1)/(2d − 1) ⌉ ≤ 2 f(d, n) ≤ dn − ( ⌊ d2 4 ⌋ +1)dn−2, which implies that f(2,n) = 2n−1,as obtained by Královič an ..."
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The feedback number f(d, n) of the Kautz undirected graph UK(d, n) is the minimum number of vertices whose removal results in an acyclic graph. This paper shows ⌈(dn+1 − dn−1 − 1d(d +1)+1)/(2d − 1) ⌉ ≤ 2 f(d, n) ≤ dn − ( ⌊ d2 4 ⌋ +1)dn−2, which implies that f(2,n) = 2n−1,as obtained by Královič andRuˇzička [Information Processing Letters 86 (4) (2003), 191–196].
Feedback numbers of Kautz digraphs �
, 2006
"... www.elsevier.com/locate/disc A subset of vertices (resp. arcs) of a graph G is called a feedback vertex (resp. arc) set of G if its removal results in an acyclic subgraph. Let f(d,n) (fa(d, n)) denote the minimum cardinality over all feedback vertex (resp. arc) sets of the Kautz digraph K(d,n). This ..."
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www.elsevier.com/locate/disc A subset of vertices (resp. arcs) of a graph G is called a feedback vertex (resp. arc) set of G if its removal results in an acyclic subgraph. Let f(d,n) (fa(d, n)) denote the minimum cardinality over all feedback vertex (resp. arc) sets of the Kautz digraph K(d,n). This paper proves that for any integers d �2 and n�1 d for n = 1,
Lower Bounds to the Size of the Minimum Feedback Vertex Sets in Splitstars ∗
"... In a graph G = (V, E), a subset F ⊂ V (G) is a feedback vertex set of G if the subgraph induced by V (G) \ F is acyclic. In this paper, we establish a lower bound to the size of the minimum feedback vertex sets in splitstars. 1 ..."
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In a graph G = (V, E), a subset F ⊂ V (G) is a feedback vertex set of G if the subgraph induced by V (G) \ F is acyclic. In this paper, we establish a lower bound to the size of the minimum feedback vertex sets in splitstars. 1