The notion of a C-ultrahomogeneous (or C-UH) graph, due to D. Isaksen et al., is adapted for digraphs and applied to the cubic distancetransitive graphs, considered as digraphs by replacing each edge by a pair of oppositely oriented arcs, with C formed by shortest oriented cycles and (k−1)-arcs with k = arc-transitivity. Moreover, (k−1)-powers of shortest cycles taken with orientation assignmen...

We consider the oriented version of a coloring game introduced by Bodlaender [On the complexity of some coloring games, Internat. J. Found. Comput. Sci. 2 (1991), 133–147]. We prove that every oriented path has oriented game chromatic number at most 7 (and this bound is tight), that every oriented tree has oriented game chromatic number at most 19 and that there exists a constant t such that ev...

Process-Aware Information System (PAIS) are IT systems that manages, supports business processes and generate large event logs from execution of business processes. An event log is represented as a tuple of the form CaseID, TimeStamp, Activity and Actor. Process Mining is an emerging area of research that deals with the study and analysis of business processes based on event logs. Process Minin...

A digraph D is traceable if it contains a path visiting every vertex, and hypotraceable if D is not traceable, but D − v is traceable for every vertex v ∈ V (D). Van Aardt, Frick, Katrenic̃ and Nielsen [Discrete Math. 11(2011), 1273-1280] showed that there exists a hypotraceable oriented graph of order n for every n > 8, except possibly for n = 9 or 11. These two outstanding existence questions ...

All triangulations of euclidean oriented matroids are of the same PLhomeomorphism type by a result of Anderson. That means all triangulations of euclidean acyclic oriented matroids are PL-homeomorphic to PL-balls and that all triangulations of totally cyclic oriented matroids are PL-homeomorphic to PLspheres. For non-euclidean oriented matroids this question is wide open. One key point in the p...

Graph grammars have been successfully used as a formalism for the speciication of realistic problems but, as far as speciication-in-the-large activities are concerned, they still have some deeciencies. In particular, most of them only support the use of at graphs, whereas for certain applications hierarchical graphs would be a more suitable modelling tool. Furthermore, there is still the need f...

All triangulations of euclidean oriented matroids are of the same PLhomeomorphism type by a result of Anderson. That means all triangulations of euclidean acyclic oriented matroids are PL-homeomorphic to PL-balls and that all triangulations of totally cyclic oriented matroids are PL-homeomorphic to PLspheres. For non-euclidean oriented matroids this question is wide open. One key point in the p...

Graph grammars have been successfully used as a formalism for the speci cation of realistic problems but, as far as speci cation-in-the-large activities are concerned, they still have some de ciencies. In particular, most of them only support the use of at graphs, whereas for certain applications hierarchical graphs would be a more suitable modelling tool. Furthermore, there is still the need f...