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bounded Tree and CliqueWidth
"... Abstract. Starting point of our work is a previous paper by Flarup, Koiran, and Lyaudet [5]. There the expressive power of certain families of polynomials is investigated. Among other things it is shown that polynomials arising as permanents of bounded treewidth matrices have the same expressivene ..."
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. Here, a monomial occurs according to whether the exponent vector satisfies a given CNF formula or not. We can in a canonical way assign a graph to such a CNF formula and speak about the treewidth of the related CNF polynomial. In this paper we show that the expressiveness of CNF polynomials of bounded
Graphs of PowerBounded CliqueWidth∗
"... Cliquewidth is a graph parameter with many algorithmic applications. For a positive integer k, the kth power of a graph G is the graph with the same vertex set as G, in which two distinct vertices are adjacent if and only if they are at distance at most k in G. Many graph algorithmic problems can ..."
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Cliquewidth is a graph parameter with many algorithmic applications. For a positive integer k, the kth power of a graph G is the graph with the same vertex set as G, in which two distinct vertices are adjacent if and only if they are at distance at most k in G. Many graph algorithmic problems can
Upper Bounds to the CliqueWidth of Graphs
 Discrete Applied Mathematics
, 1997
"... A graph complexity measure that we call cliquewidth is associated in a natural way with certain graph decompositions, more or less like treewidth is associated with treedecomposition which are, actually, hierarchical decompositions of graphs. In general, a decomposition of a graph G can be viewe ..."
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Cited by 67 (16 self)
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A graph complexity measure that we call cliquewidth is associated in a natural way with certain graph decompositions, more or less like treewidth is associated with treedecomposition which are, actually, hierarchical decompositions of graphs. In general, a decomposition of a graph G can
A SAT Approach to CliqueWidth
"... Cliquewidth is a graph invariant that has been widely studied in combinatorics and computational logic. Computing the cliquewidth of a graph is an intricate problem, the exact cliquewidth is not known even for very small graphs. We present a new method for computing cliquewidth via an encoding t ..."
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Cliquewidth is a graph invariant that has been widely studied in combinatorics and computational logic. Computing the cliquewidth of a graph is an intricate problem, the exact cliquewidth is not known even for very small graphs. We present a new method for computing cliquewidth via an encoding
CliqueWidth and Parity Games
, 2007
"... The question of the exact complexity of solving parity games is one of the major open problems in system verification, as it is equivalent to the problem of modelchecking the modal µcalculus. The known upper bound is NP∩coNP, but no polynomial algorithm is known. It was shown that on treelike g ..."
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Cited by 15 (0 self)
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like graphs (of bounded treewidth and DAGwidth) a polynomialtime algorithm does exist. Here we present a polynomialtime algorithm for parity games on graphs of bounded cliquewidth (class of graphs containing e.g. complete bipartite graphs and cliques), thus completing the picture. This also extends
Computing the Tutte polynomial on graphs of bounded cliquewidth
 SIAM Journal on Discrete Mathematics
, 2006
"... Abstract. The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only for a few special graph classes, like for those of bounded treewidth. The notion of cliquewidth extends the definition of cograhs (graphs without induced P4), and it is a more gener ..."
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Cited by 15 (0 self)
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general notion than that of treewidth. We show a subexponential algorithm (running in time exp O(n 1−ε) ) for computing the Tutte polynomial on graphs of bounded cliquewidth. In fact, our algorithm computes the more general Upolynomial.
New Graph Classes of Bounded CliqueWidth
, 2003
"... Cliquewidth of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every problem expressible in a certain kind of Monadic Second Order Logic called LinEMSOL(τ1,L ) by Courcelle, Makowsky and Rotics, is lineartime solvable on any graph class with bounded c ..."
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Cited by 5 (0 self)
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Cliquewidth of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every problem expressible in a certain kind of Monadic Second Order Logic called LinEMSOL(τ1,L ) by Courcelle, Makowsky and Rotics, is lineartime solvable on any graph class with bounded
CliqueWidth of Unit Interval Graphs
, 709
"... The cliquewidth is known to be unbounded in the class of unit interval graphs. In this paper, we show that this is a minimal hereditary class of unbounded cliquewidth, i.e., in every hereditary subclass of unit interval graphs the cliquewidth is bounded by a constant. Keywords: Unit interval grap ..."
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Cited by 2 (0 self)
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The cliquewidth is known to be unbounded in the class of unit interval graphs. In this paper, we show that this is a minimal hereditary class of unbounded cliquewidth, i.e., in every hereditary subclass of unit interval graphs the cliquewidth is bounded by a constant. Keywords: Unit interval
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
On the CliqueWidth of Graphs with Few P 4 s
, 1998
"... Babel and Olariu (1995) introduced the class of (q; t) graphs in which every set of q vertices has at most t distinct induced P 4 s. Graphs of cliquewidth at most k were introduced by Courcelle, Engelfriet and Rozenberg (1993) as graphs which can be defined by k expressions based on graph operati ..."
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Cited by 3 (1 self)
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Babel and Olariu (1995) introduced the class of (q; t) graphs in which every set of q vertices has at most t distinct induced P 4 s. Graphs of cliquewidth at most k were introduced by Courcelle, Engelfriet and Rozenberg (1993) as graphs which can be defined by k expressions based on graph
Results 1  10
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111,667