-
01/2010; Springer., ISBN: 978-3-642-04499-1
-
Discrete Applied Mathematics. 01/2009; 157:583-595.
-
Graph-Theoretic Concepts in Computer Science, 35th International Workshop, WG 2009, Montpellier, France, June 24-26, 2009. Revised Papers; 01/2009
-
Frank Gurski
[show abstract]
[hide abstract]
ABSTRACT: In this paper we compare and illustrate the algorithmic use of graphs of bounded tree-width and graphs of bounded clique-width. For this purpose we give polynomial time algorithms for computing the four basic graph parameters independence number, clique number, chromatic number, and clique covering number on a given tree structure of graphs of bounded tree-width and graphs of bounded clique-width in polynomial time. We also present linear time algorithms for computing the latter four basic graph parameters on trees, i.e. graphs of tree-width 1, and on co-graphs, i.e. graphs of clique-width at most 2.
07/2008;
-
[show abstract]
[hide abstract]
ABSTRACT: The k-power graph of a graph G is the graph in which two vertices are adjacent if and only if there is a path between them in G of length at most k. We show that (1.) the k-power graph of a tree has NLC-width at most k + 2 and clique-width at most
k+2+max(ë\frack2û-1,0)k+2+\max(\lfloor \frac{k}{2}\rfloor -1,0)
, (2.) the k-leaf-power graph of a tree has NLC-width at most k and clique-width at most
k+ max(ë\frack2û-2,0)k+ \max(\lfloor \frac{k}{2}\rfloor -2,0)
, and (3.) the k-power graph of a graph of tree-width l has NLC-width at most (k + 1)
l + 1− 1 and clique-width at most 2·(k + 1)
l + 1− 2.
12/2007: pages 76-85;
-
Frank Gurski
[show abstract]
[hide abstract]
ABSTRACT: In this paper we consider module-composed graphs, i.e. graphs which can be defined by a sequence of one-vertex insertions v_1,...,v_n, such that the neighbourhood of vertex v_i, 2<= i<= n, forms a module (a homogeneous set) of the graph defined by vertices v_1,..., v_{i-1}. We show that module-composed graphs are HHDS-free and thus homogeneously orderable, weakly chordal, and perfect. Every bipartite distance hereditary graph, every (co-2C_4,P_4)-free graph and thus every trivially perfect graph is module-composed. We give an O(|V_G|(|V_G|+|E_G|)) time algorithm to decide whether a given graph G is module-composed and construct a corresponding module-sequence. For the case of bipartite graphs, module-composed graphs are exactly distance hereditary graphs, which implies simple linear time algorithms for their recognition and construction of a corresponding module-sequence.
06/2007;
-
Frank Gurski
[show abstract]
[hide abstract]
ABSTRACT: In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [BNS02] denoted as the MRSO problem. The problem is known to be NP-complete for planar associated implied structure graphs of vertex degree at most 3. In [BFHV05] a first polynomial dynamic programming algorithms for MRSO on implied structure graphs with maximum vertex degree 3 of bounded cut-width is shown. We give a simple but more general polynomial dynamic programming solution for the MRSO problem for associated implied structure graphs of bounded clique-width. Our result implies that MRSO is polynomial for graphs of bounded tree-width, co-graphs, $P_4$-sparse graphs, and distance hereditary graphs. Further we conclude that the problem of comparing two solutions for MRSO is hard for the class of problems which can be solved in polynomial time with a number of parallel queries to an oracle in NP.
05/2007;
-
Frank Gurski
[show abstract]
[hide abstract]
ABSTRACT: In this paper we survey the behavior of various graph operations on the graph parameters clique-width and NLC-width. We give upper and lower bounds for the clique-width and NLC-width of the modified graphs in terms of the clique-width and NLC-width of the involved graphs. Therefor we consider the binary graph operations join, co-join, sum, difference, products, corona, substitution, and 1-sum, and the unary graph operations quotient, subgraph, edge complement, bipartite edge complement, power of graphs, switching, local complementation, edge addition, edge subdivision, vertex identification, and vertex addition.
03/2007;
-
Discrete Mathematics. 01/2007; 307:756-759.
-
Discrete Mathematics. 01/2007; 307:2734-2754.
-
Theor. Comput. Sci. 01/2006; 359:188-199.
-
Graph-Theoretic Concepts in Computer Science, 31st International Workshop, WG 2005, Metz, France, June 23-25, 2005, Revised Selected Papers; 01/2005
-
[show abstract]
[hide abstract]
ABSTRACT: We show that l vertex disjoint paths between l pairs of vertices can be found in linear time for co-graphs but is NP-complete for graphs of NLC-width at most 4 and clique-width
at most 7. This is the first inartificial graph problem known to be NP-complete on graphs of bounded clique-width but solvable
in linear time on co-graphs and graphs of bounded tree-width.
03/2004: pages 119-128;
-
LATIN 2004: Theoretical Informatics, 6th Latin American Symposium, Buenos Aires, Argentina, April 5-8, 2004, Proceedings; 01/2004
-
[show abstract]
[hide abstract]
ABSTRACT: We show that there exists a linear time algorithm for deciding whether a graph of bounded tree-width has clique-width k for some fixed integer k.
09/2003;
-
[show abstract]
[hide abstract]
ABSTRACT: We show that many non-MSO1 NP-hard graph problems can be solved in polynomial time on clique-width and NLC-width bounded graphs using a very general and simple scheme. Our examples are partition into cliques, partition into triangles, partition into complete bipartite subgraphs, partition into perfect matchings, partition into forests, cubic subgraph, Hamiltonian path, minimum maximal matching, and vertex/edge separation problems. 1
07/2001;
-
[show abstract]
[hide abstract]
ABSTRACT: We introduce the class of k-node label controlled (k-NLC) graphs and the class of k-NLC trees. Each k-NLC graph is an undirected tree-structured graph, where k is a positive integer. The class of k-NLC trees is a proper subset of the class of k-NLC graphs. Both classes include many interesting graph families. For instance, each partial k-tree is a (2 k+1 Gamma 1)-NLC tree and each co-graph is a 1-NLC graph. Furthermore, we introduce a very general method for the design of polynomial algorithms for NP-complete graph problems, where the input graphs are restricted to tree-structured graphs. We exemplify our method with the simple max-cut problem and the Hamiltonian circuit property on k-NLC graphs. 1 Introduction A large number of papers have been published concerning special classes of tree-structured graphs. A well-known and extensively studied class of tree-structured graphs is the class of k-trees [Ros74] and partial k-trees which is equivalent to the class of graphs having tr...
09/2000;
-
Frank Gurski
[show abstract]
[hide abstract]
ABSTRACT: . We proof that every graph of clique-width k which does not contain the complete bipartite graph Kn;n for some n > 1 as a subgraph has tree-width at most 3k(n 1) 1. This immediately implies that a set of graphs of bounded clique-width has bounded tree-width if it is uniformly l-sparse, closed under subgraphs, of bounded degree, or planar. 1 Introduction The clique-width of a graph is dened by composition mechanisms for vertexlabeled graphs, see [CO00]. The operations are the vertex disjoint union of labeled graphs, the addition of edges between vertices controlled by some label pair, and a relabeling of the vertices. The used number of labels corresponds to the clique-width of the dened graph. Clique-width bounded graphs are especially interesting from an algorithmic point of view. A lot of NP-complete graph problems can be solved in polynomial time for graphs of bounded clique-width if the composition tree of the graphs is explicitly given. For example, the set of all graph p...
09/2000;
-
Graph-Theoretic Concepts in Computer Science, 26th International Workshop, WG 2000, Konstanz, Germany, June 15-17, 2000, Proceedings; 01/2000
-
[show abstract]
[hide abstract]
ABSTRACT: In this paper, we consider NLC-width, NLCT-width, and linear NLC-width bounded graphs. We show that the set of all complete binary trees has unbounded linear NLC-width and that the set of all co-graphs has unbounded NLCT-width. Since trees have NLCT-width 3 and co-graphs have NLC-width 1, it follows that the family of linear NLC-width bounded graph classes is a proper subfamily of the family of NLCT-width bounded graph classes and that the family of NLCT-width bounded graph classes is a proper subfamily of the family of NLC-width bounded graph classes.
Theoretical Computer Science.
