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853
Isomorphism for graphs of bounded feedback vertex set number
, 2009
"... This paper presents an O(n 2) algorithm for deciding isomorphism of graphs that have bounded feedback vertex set number. This number is defined as the minimum number of vertex deletions required to obtain a forest. Our result implies that Graph Isomorphism is fixedparameter tractable with respect t ..."
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Cited by 12 (3 self)
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This paper presents an O(n 2) algorithm for deciding isomorphism of graphs that have bounded feedback vertex set number. This number is defined as the minimum number of vertex deletions required to obtain a forest. Our result implies that Graph Isomorphism is fixedparameter tractable with respect
Graph isomorphism parameterized by feedback vertex set number is fixedparameter tractable
, 2009
"... ..."
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
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
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Cited by 357 (6 self)
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to design the first polynomialtime (polylog ntimesoptimal) approximation algorithms for wellknown NPhard optimization problems such as graph partitioning, mincut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems
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
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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Cited by 1 (1 self)
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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
Feedback vertex set on ATfree graphs
, 2007
"... We present a polynomial time algorithm to compute a minimum (weight) feedback vertex set for ATfree graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number. ..."
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Cited by 4 (0 self)
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We present a polynomial time algorithm to compute a minimum (weight) feedback vertex set for ATfree graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number.
Bounding the Feedback Vertex Number of Digraphs in Terms of Vertex Degrees
"... The Turán bound [17] is a famous result in graph theory, which relates the independence number of an undirected graph to its edge density. Also the Caro–Wei inequality [4, 18], which gives a more refined bound in terms of the vertex degree sequence of a graph, might be regarded today as a classical ..."
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Cited by 1 (0 self)
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result. We show how these statements can be generalized to directed graphs, thus yielding a bound on directed feedback vertex number in terms of vertex outdegrees and in terms of average outdegree, respectively. Keywords: directed feedback vertex number, Caro–Wei inequality, feedback set, acyclic set
BOUNDS ON THE NUMBER OF VERTEX INDEPENDENT SETS IN A GRAPH
, 2006
"... We consider the number of vertex independent sets i(G). In general, the problem of determining the value of i(G) is NPcomplete. We present several upper and lower bounds for i(G) in terms of order, size or independence number. We obtain improved bounds for i(G) on restricted graph classes such as ..."
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Cited by 8 (0 self)
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We consider the number of vertex independent sets i(G). In general, the problem of determining the value of i(G) is NPcomplete. We present several upper and lower bounds for i(G) in terms of order, size or independence number. We obtain improved bounds for i(G) on restricted graph classes
Bounded Color Multiplicity Graph Isomorphism is in the #L Hierarchy
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 121 (2004)
, 2004
"... In this paper we study the complexity of Bounded Color Multiplicity Graph Isomorphism BCGIb: the input is a pair of vertexcolored graphs such that the number of vertices of a given color in an input graph is bounded by b. We show that BCGIb is in the #L hierarchy (more precisely, the ModkL hierarch ..."
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Cited by 5 (2 self)
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In this paper we study the complexity of Bounded Color Multiplicity Graph Isomorphism BCGIb: the input is a pair of vertexcolored graphs such that the number of vertices of a given color in an input graph is bounded by b. We show that BCGIb is in the #L hierarchy (more precisely, the Modk
Results 1  10
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853