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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
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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classes of powerunbounded cliquewidth and give a sufficient condition for cliquewidth to be powerbounded. Based on this condition, we characterize graph classes of powerbounded cliquewidth among classes defined by two connected forbidden induced subgraphs. We also show that for every integer k
Cliquewidth and the speed of hereditary properties
"... In this paper, we study the relationship between the number of nvertex graphs in a hereditary class X, also known as the speed of the class X, and boundedness of the cliquewidth in this class. We show that if the speed of X is faster than n!c n for any c, then the cliquewidth of graphs in X is un ..."
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Cited by 4 (3 self)
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In this paper, we study the relationship between the number of nvertex graphs in a hereditary class X, also known as the speed of the class X, and boundedness of the cliquewidth in this class. We show that if the speed of X is faster than n!c n for any c, then the cliquewidth of graphs in X
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
CliqueWidth Of Countable Graphs: A Compactness Property
 DISCRETE MATHEMATICS
, 2000
"... We define the cliquewidth of a countable graph. We prove that a countable graph has finite cliquewidth iff its finite induced subgraphs have cliquewidth at most k for some integer k. ..."
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Cited by 12 (5 self)
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We define the cliquewidth of a countable graph. We prove that a countable graph has finite cliquewidth iff its finite induced subgraphs have cliquewidth at most k for some integer k.
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
, 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
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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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
Results 1  10
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