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269,877
Linear time solvable optimization problems on graphs of bounded cliquewidth
, 2000
"... Hierarchical decompositions of graphs are interesting for algorithmic purposes. There are several types of hierarchical decompositions. Tree decompositions are the best known ones. On graphs of treewidth at most k, i.e., that have tree decompositions of width at most k, where k is fixed, every dec ..."
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Cited by 168 (22 self)
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decision or optimization problem expressible in monadic secondorder logic has a linear algorithm. We prove that this is also the case for graphs of cliquewidth at most k, where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer
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
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
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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as the class of graphs which can be dened by expressions based on graph operations which use k vertex labels (i.e. k expressions). Given a graph G of bounded clique width, say k, Courcelle, Makowsky and Rotics have shown in [2] that there are linear time solutions for a number of optimization problems on G
Cliquewidth: On the Price of Generality
, 2009
"... Many hard problems can be solved efficiently when the input is restricted to graphs of bounded treewidth. By the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the treewidth of the input graph. Moreo ..."
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Cited by 11 (1 self)
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. Moreover, for every fixed k ≥ 0, such problems can be solved in linear time on graphs of treewidth at most k. In particular, this implies that basic problems like Dominating Set, Graph Coloring, Clique, and Hamiltonian Cycle are solvable in linear time on graphs of bounded treewidth. A significant amount
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
ALMOST OPTIMAL LOWER BOUNDS FOR PROBLEMS PARAMETERIZED BY CLIQUEWIDTH∗
"... Abstract. We obtain asymptotically tight algorithmic bounds for MaxCut and Edge Dominating Set problems on graphs of bounded cliquewidth. We show that on an nvertex graph of cliquewidth t both problems (1) cannot be solved in time f(t)no(t) for any function f of t unless exponential time hypoth ..."
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Abstract. We obtain asymptotically tight algorithmic bounds for MaxCut and Edge Dominating Set problems on graphs of bounded cliquewidth. We show that on an nvertex graph of cliquewidth t both problems (1) cannot be solved in time f(t)no(t) for any function f of t unless exponential time
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
Results 1  10
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269,877