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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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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 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
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
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
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
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
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
Results 1  10
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