Results 1  10
of
1,438,240
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 ..."
Abstract
 Add to MetaCart
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
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 ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 67 (16 self)
 Add to MetaCart
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
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 ..."
Abstract
 Add to MetaCart
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
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 ..."
Abstract
 Add to MetaCart
. 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
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 ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
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
Results 1  10
of
1,438,240