21 research outputs found
On the relationship between NLC-width and linear NLC-width
AbstractIn 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
Decision problems for node label controlled graph grammars
AbstractTwo basic techniques are presented to show the decidability status of a number of problems concerning node label controlled graph grammars. Most of the problems are of graph-theoretic nature and concern topics like planarity, connectedness and bounded degreeness of graph languages
Line graphs of bounded clique-width
AbstractWe show that a set of graphs has bounded tree-width or bounded path-width if and only if the corresponding set of line graphs has bounded clique-width or bounded linear clique-width, respectively. This relationship implies some interesting algorithmic properties and re-proves already known results in a very simple way. It also shows that the minimization problem for NLC-width is NP-complete
Algorithmic Meta-Theorems
Algorithmic meta-theorems are general algorithmic results applying to a whole
range of problems, rather than just to a single problem alone. They often have
a "logical" and a "structural" component, that is they are results of the form:
every computational problem that can be formalised in a given logic L can be
solved efficiently on every class C of structures satisfying certain
conditions. This paper gives a survey of algorithmic meta-theorems obtained in
recent years and the methods used to prove them. As many meta-theorems use
results from graph minor theory, we give a brief introduction to the theory
developed by Robertson and Seymour for their proof of the graph minor theorem
and state the main algorithmic consequences of this theory as far as they are
needed in the theory of algorithmic meta-theorems
Double Greibach operator grammars
AbstractEvery context-free grammar can be transformed into one in double Greibach operator form, that satisfies both double Greibach form and operator form. Examination of the expressive power of various well-known subclasses of context-free grammars in double Greibach and/or operator form yields an extended hierarchy of language classes. Basic decision properties such as equivalence can be stated in stronger forms via new classes of languages in this hierarchy
On the Monadic Second-Order Transduction Hierarchy
We compare classes of finite relational structures via monadic second-order
transductions. More precisely, we study the preorder where we set C \subseteq K
if, and only if, there exists a transduction {\tau} such that
C\subseteq{\tau}(K). If we only consider classes of incidence structures we can
completely describe the resulting hierarchy. It is linear of order type
{\omega}+3. Each level can be characterised in terms of a suitable variant of
tree-width. Canonical representatives of the various levels are: the class of
all trees of height n, for each n \in N, of all paths, of all trees, and of all
grids