— It is an intriguing question to see what kind of information on the structure of an oriented graph D one can obtain if D does not contain a fixed oriented graph H as a subgraph. The related question in the unoriented case has been an active area of research, and is relatively well-understood in the theory of quasi-random graphs and extremal combinatorics. In this paper, we consider the simple...

We prove a number of auxiliary facts about graphs, mainly about vertex sequences of chains and oriented chains. Then we define a graph to be well-founded if for each vertex in the graph the length of oriented chains ending at the vertex is bounded. A well-founded graph does not have directed cycles or infinite descending chains. In the second part of the article we prove some auxiliary facts ab...

Given a group or semi-group Γ generated (in the sense of semi-groups) by some subset S ⊂ Γ, the Cayley graph of Γ with respect to S is the oriented graph having vertices γ ∈ Γ and oriented edges (γ, γs)s∈S . In this paper, we consider generating sets S which are not necessarily finite thus yielding oriented Cayley graphs which are perhaps not locally finite. The above situation gives rise to a ...

Let X be a finite graph, with edges colored and possibly oriented, such that an oriented edge and a non-oriented one cannot have same color. The universal Hopf algebra H(X) coacting on X is in general non commutative, infinite dimensional, bigger than the algebra of functions on the usual symmetry group G(X). For a graph with no edges Tannakian duality makes H(X) correspond to a Temperley-Lieb ...

Thomassen recently introduced the concept of a nitely spreading graph: an innnite graph whose edges can be oriented, each in one, both, or neither direction, so that every vertex has nite out-degree and every ray has a forward oriented tail. He conjectured that a graph is nitely spreading if and only if it is bounded|equivalently, if it contains none of three speciied innnitely spreading graphs...

An infinite graph is called bounded if for every labelling of its vertices with natural numbers there exists a sequence of natural numbers which eventually exceeds the labelling along any ray in the graph. Thomassen has conjectured that a countable graph is bounded if and only if its edges can be oriented, possibly both ways, so that every vertex has finite out-degree and every ray has a forwar...

We prove a number of auxiliary facts about graphs, mainly about vertex sequences of chains and oriented chains. Then we define a graph to be well-founded if for each vertex in the graph the length of oriented chains ending at the vertex is bounded. A wellfounded graph does not have directed cycles or infinite descending chains. In the second part of the article we prove some auxiliary facts abo...

Program slicing can be very useful for understanding and debugging aspect-oriented programs. Program slicing is a common technique, but it is not trivial to use in aspectoriented programming. Current implementations of slicing tools lack support for features of popular aspect-oriented languages. This paper proposes a detailed algorithm for the construction of an aspect-oriented system dependenc...

Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems involved in such a difficult field, a very special role is played by graph classification issues. We propose new techniques devised to help the designer and th...

Much recent research work discusses the transformation between different process modelling languages. This work, however, is mainly focussed on specific process modelling languages, and thus the general reusability of the applied transformation concepts is rather limited. In this paper, we aim to abstract from concrete transformation strategies by distinguishing two major paradigms for represen...