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452
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
A note on cliquewidth and treewidth on structures
, 2008
"... We give a simple proof that the straightforward generalisation of cliquewidth to arbitrary structures can be unbounded on structures of bounded treewidth. This can be corrected by allowing fusion of elements. ..."
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Cited by 2 (0 self)
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We give a simple proof that the straightforward generalisation of cliquewidth to arbitrary structures can be unbounded on structures of bounded treewidth. This can be corrected by allowing fusion of elements.
The TreeWidth of CliqueWidth Bounded Graphs Without K n,n
 In Proceedings of GraphTheoretical Concepts in Computer Science, volume 1938 of LNCS
, 2000
"... . We proof that every graph of cliquewidth k which does not contain the complete bipartite graph Kn;n for some n > 1 as a subgraph has treewidth at most 3k(n 1) 1. This immediately implies that a set of graphs of bounded cliquewidth has bounded treewidth if it is uniformly lsparse, close ..."
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Cited by 21 (3 self)
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. We proof that every graph of cliquewidth k which does not contain the complete bipartite graph Kn;n for some n > 1 as a subgraph has treewidth at most 3k(n 1) 1. This immediately implies that a set of graphs of bounded cliquewidth has bounded treewidth if it is uniformly l
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
Graph Operations on CliqueWidth Bounded Graphs
, 2008
"... In this paper we survey the behavior of various graph operations on the graph parameters cliquewidth and NLCwidth. We give upper and lower bounds for the cliquewidth and NLCwidth of the modified graphs in terms of the cliquewidth and NLCwidth of the involved graphs. Therefor we consider the bi ..."
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Cited by 4 (0 self)
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In this paper we survey the behavior of various graph operations on the graph parameters cliquewidth and NLCwidth. We give upper and lower bounds for the cliquewidth and NLCwidth of the modified graphs in terms of the cliquewidth and NLCwidth of the involved graphs. Therefor we consider
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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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
Cliquewidth and edge contraction
, 2013
"... We prove that edge contractions do not preserve the property that a set of graphs has bounded cliquewidth. ..."
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Cited by 1 (0 self)
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We prove that edge contractions do not preserve the property that a set of graphs has bounded cliquewidth.
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