Results 1  10
of
146,026
Computing the Tutte polynomial on graphs of bounded cliquewidth
 SIAM Journal on Discrete Mathematics
, 2006
"... Abstract. The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only for a few special graph classes, like for those of bounded treewidth. The notion of cliquewidth extends the definition of cograhs (graphs without induced P4), and it is a more gener ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
general notion than that of treewidth. We show a subexponential algorithm (running in time exp O(n 1−ε) ) for computing the Tutte polynomial on graphs of bounded cliquewidth. In fact, our algorithm computes the more general Upolynomial.
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
Computing graph polynomials on graphs of bounded cliquewidth
 GraphTheoretic Concepts in Computer Science, 32nd International Workshop, WG 2006
"... Abstract. We discuss the complexity of computing various graph polynomials of graphs of fixed cliquewidth. We show that the chromatic polynomial, the matching polynomial and the twovariable interlace polynomial of a graph G of cliquewidth at most k with n vertices can be computed in time O(n f(k) ..."
Abstract

Cited by 13 (5 self)
 Add to MetaCart
Abstract. We discuss the complexity of computing various graph polynomials of graphs of fixed cliquewidth. We show that the chromatic polynomial, the matching polynomial and the twovariable interlace polynomial of a graph G of cliquewidth at most k with n vertices can be computed in time O(n f
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
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
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 and edge contraction
, 2013
"... We prove that edge contractions do not preserve the property that a set of graphs has bounded cliquewidth. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We prove that edge contractions do not preserve the property that a set of graphs has bounded cliquewidth.
A multivariate interlace polynomial and its computation for graphs
"... of bounded cliquewidth ..."
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
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 ..."
Abstract
 Add to MetaCart
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
Results 1  10
of
146,026