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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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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.
Computing graph polynomials on graphs of bounded cliquewidth
 GraphTheoretic Concepts in Computer Science, 32nd International Workshop, WG 2006
"... Abstract. We discuss the complexity of computing various graph polynomials of graphs of fixed cliquewidth. We show that the chromatic polynomial, the matching polynomial and the twovariable interlace polynomial of a graph G of cliquewidth at most k with n vertices can be computed in time O(n f(k) ..."
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Abstract. We discuss the complexity of computing various graph polynomials of graphs of fixed cliquewidth. We show that the chromatic polynomial, the matching polynomial and the twovariable interlace polynomial of a graph G of cliquewidth at most k with n vertices can be computed in time O(n f
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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be expressed in terms of graph powers. We initiate the study of graph classes of powerbounded cliquewidth. A graph class is said to be of powerbounded cliquewidth if there exists an integer k such that the kth powers of graphs in the class form a class of bounded cliquewidth. We identify several graph
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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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
Decompositionwidth: Extending the Cliquewidth to Hypergraphs
"... Abstract. We define a width parameter for hypergraphs, which we call the decompositionwidth. We provide an explicit family of hypergraphs of large decompositionwidth and we prove that every MSO property can be checked in linear time for hypergraphs with bounded decompositionwidth when their decom ..."
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their decomposition is given. Finally, the decompositionwidth of a graph is proved to be bounded by twice its cliquewidth, which suggests that decompositionwidth is a generalization of cliquewidth to relations of large or unbounded arity. 1
Computing the cliquewidth of Cactus graphs
"... Abstract. Similar to the treewidth (twd), the cliquewidth (cwd) is an invariant of graphs. A well known relationship between treewidth and cliquewidth is that cwd(G) ≤ 3 · 2 twd(G)−1 . It is also known that treewidth of Cactus graphs is 2, therefore the cliquewidth for those graphs is smaller ..."
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or equal than 6. In this paper, it is shown that the cliquewidth of Cactus graphs is smaller or equal to 4 and we present a polynomial time algorithm which computes exactly a 4expression.
Results 1  10
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