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Feedback Vertex Sets in Tournaments
, 2010
"... We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an nvertex tournament. We prove that every tournament on n vertices ..."
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We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an nvertex tournament. We prove that every tournament on n vertices
Feedback Vertex set and longest . . .
"... We present a polynomial time algorithm to compute a minimum (weight) feedback vertex setfor ATfree graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number.We also present an O(nm²) algorithm to ..."
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We present a polynomial time algorithm to compute a minimum (weight) feedback vertex setfor ATfree graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number.We also present an O(nm²) algorithm to
Parameterized algorithms for feedback vertex set
 in Proc. 1st Int. Workshop on Parameterized and Exact Computation, IWPEC 2004
"... Abstract. We present an algorithm for the parameterized feedback vertex set problem that runs in time O((2 lg k + 2 lg lg k + 18) k n 2). This improves the previous O(max{12 k, (4 lg k) k}n ω) algorithm by Raman et al. by roughly a 2 k factor (n w ∈ O(n 2.376) is the time needed to multiply two n × ..."
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Cited by 15 (0 self)
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Abstract. We present an algorithm for the parameterized feedback vertex set problem that runs in time O((2 lg k + 2 lg lg k + 18) k n 2). This improves the previous O(max{12 k, (4 lg k) k}n ω) algorithm by Raman et al. by roughly a 2 k factor (n w ∈ O(n 2.376) is the time needed to multiply two n
Enumeration of Trees by VertexSet Partitions
, 1995
"... Generating functions are given for labeled tree enumeration by the number of edges with a specific color in a 2color scheme, or equivalently, the number of vertexset partitions. Two cases are considered, one with each tree assigned a unit weight and the other with vertexorder weight factors. ..."
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Generating functions are given for labeled tree enumeration by the number of edges with a specific color in a 2color scheme, or equivalently, the number of vertexset partitions. Two cases are considered, one with each tree assigned a unit weight and the other with vertexorder weight factors.
Feedback Vertex Set in Mixed Graphs
"... Abstract. A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph onnvertices contains a feedback vertex set (FVS) of size at mostk, in time47.5 k ·k!·O(n 4). This is the first fixed parameter tractable algorithm for FVS that ..."
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Cited by 5 (0 self)
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Abstract. A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph onnvertices contains a feedback vertex set (FVS) of size at mostk, in time47.5 k ·k!·O(n 4). This is the first fixed parameter tractable algorithm for FVS
Vertex Set Partitions Preserving Conservativeness
, 2000
"... Let G be an undirected graph and P=[X 1,..., X n] be a partition of V(G). Denote by G P the graph which has vertex set [X 1,..., X n], edge set E, and is obtained from G by identifying vertices in each class X i of the partition P. Given a conservative graph (G, w), we study vertex set partitions pr ..."
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Cited by 1 (1 self)
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Let G be an undirected graph and P=[X 1,..., X n] be a partition of V(G). Denote by G P the graph which has vertex set [X 1,..., X n], edge set E, and is obtained from G by identifying vertices in each class X i of the partition P. Given a conservative graph (G, w), we study vertex set partitions
Perestroikas of vertex sets at umbilic points
, 2008
"... Mark all vertices on a curve evolving under a family of curves obtained by intersecting a smooth surface M with the 1parameter family of planes parallel to the tangent plane of M at a point p. Those vertices trace out a set, called the vertex set through p. We take p to be a generic umbilic point o ..."
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Mark all vertices on a curve evolving under a family of curves obtained by intersecting a smooth surface M with the 1parameter family of planes parallel to the tangent plane of M at a point p. Those vertices trace out a set, called the vertex set through p. We take p to be a generic umbilic point
Improved algorithms for feedback vertex set problems
 J. Comput. Syst. Sci
"... Abstract. We present improved parameterized algorithms for the Feedback Vertex Set problem on both unweighted and weighted graphs. Both algorithms run in time O(5 k kn 2 ). The algorithms construct a feedback vertex set of size bounded by k (in the weighted case this set is of minimum weight among ..."
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Cited by 42 (9 self)
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Abstract. We present improved parameterized algorithms for the Feedback Vertex Set problem on both unweighted and weighted graphs. Both algorithms run in time O(5 k kn 2 ). The algorithms construct a feedback vertex set of size bounded by k (in the weighted case this set is of minimum weight among
Greedoids on Vertex Sets of Unicycle Graphs
, 2009
"... A maximum stable set in a graph G is a stable set of maximum size. S is a local maximum stable set of G, and we write S ∈ Ψ(G), if S is a maximum stable set of the subgraph spanned by S ∪ N(S), where N(S) is the neighborhood of S. G is a unicycle graph if it owns only one cycle. In [10] we have show ..."
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shown that the family Ψ(T) of a forest T forms a greedoid on its vertex set. Bipartite, trianglefree, and wellcovered graphs G whose Ψ(G) form greedoids were analyzed in [11, 12, 16], respectively. In this paper we characterize the unicycle graphs whose families of local maximum stable sets form
A cubic kernel for feedback vertex set
, 2006
"... Abstract. In this paper, it is shown that the Feedback Vertex Set problem on unweighted, undirected graphs has a kernel of cubic size. I.e., a polynomial time algorithm is described, that, when given a graph G andanintegerk, finds a graph H and integer k ′ ≤ k, such that H has a feedback vertex set ..."
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Cited by 27 (6 self)
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Abstract. In this paper, it is shown that the Feedback Vertex Set problem on unweighted, undirected graphs has a kernel of cubic size. I.e., a polynomial time algorithm is described, that, when given a graph G andanintegerk, finds a graph H and integer k ′ ≤ k, such that H has a feedback vertex
Results 1  10
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6,263