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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
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
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
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
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 66 (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 of full bubble model graphs
, 2013
"... A bubble model is a 2dimensional representation of proper interval graphs. We consider proper interval graphs that have bubble models of specific properties. We characterise the maximal such proper interval graphs of bounded cliquewidth and of bounded linear cliquewidth and the minimal such proper ..."
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Cited by 1 (1 self)
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A bubble model is a 2dimensional representation of proper interval graphs. We consider proper interval graphs that have bubble models of specific properties. We characterise the maximal such proper interval graphs of bounded cliquewidth and of bounded linear cliquewidth and the minimal
Reasoning in Argumentation Frameworks of Bounded CliqueWidth
, 2010
"... Most computational problems in the area of abstract argumentation are intractable, thus identifying tractable fragments and developing efficient algorithms for such fragments are important objectives towards practically efficient argumentation systems. One approach to tractability is to view abstrac ..."
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abstract argumentation frameworks (AFs) as directed graphs and bound certain graph parameters. In particular, Dunne showed that many problems can be solved in linear time for AFs of bounded treewidth. In this paper we consider the graphparameter cliquewidth, which is more general than treewidth
Results 1  10
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294,452