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On the Linear Structure and CliqueWidth of Bipartite Permutation Graphs
, 2001
"... Bipartite permutation graphs have several nice characterizations in terms of vertex ordering. Besides, as ATfree graphs, they have a linear structure in the sense that any connected bipartite permutation graph has a dominating path. In the present paper, we elaborate the linear structure of bipa ..."
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Cited by 17 (4 self)
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of bipartite permutation graphs by showing that any connected graph in the class can be stretched into a "path" with "edges" being chain graphs. A particular consequence from the obtained characterization is that the cliquewidth of bipartite permutation graphs is unbounded, which
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
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
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
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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at most k iff it has a decomposition defined in terms of k operations. Hierarchical graph decompositions are interesting for algorithmic purposes. In fact, many NPcomplete problems have linear algorithms on graphs of treewidth or of cliquewidth bounded by some fixed k, and the same will hold for graphs
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
New Graph Classes of Bounded CliqueWidth II
, 2003
"... Cliquewidth of graphs is a major new concept with respect to eciency of graph algorithms. It is known that every problem expressible in a certain kind of Monadic Second Order Logic, called LinEMSOL( 1;L ) by Courcelle, Makowsky and Rotics, is lineartime solvable on any graph class with bounded ..."
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Cliquewidth of graphs is a major new concept with respect to eciency of graph algorithms. It is known that every problem expressible in a certain kind of Monadic Second Order Logic, called LinEMSOL( 1;L ) by Courcelle, Makowsky and Rotics, is lineartime solvable on any graph class with bounded
Cliquewidth of Partner limited graphs
, 2000
"... The cliquewidth of a graph G is the minimum number of labels that are required for dening G by an expression based on graph operations using vertex labels. The Partner limited graphs (PLgraphs for short) are dened to be graphs with a limited number of P 4 's. We prove that PLgraphs are of b ..."
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are of bounded cliquewidth. It follows that a large number of optimization problems have polynomial solutions for this family of graphs. Key words: Clique width, graph decomposition, bipartite. 1 Introduction In [1], Courcelle, Engelfriet and Rozenberg have dened the class of graphs of cliquewidth at most k
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
Results 1  10
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3,475