This work aims to extend the algebraical approach to graph transformation to model object-oriented systems structures and computations. A graph grammar based formal framework for object-oriented system modeling is presented, incorporating both the static aspects of system modeling and the dynamic aspects of computation of objectoriented programs.

We consider the complexity of oriented homomorphism and two of its variants, namely strong oriented homomorphism and pushable homomorphism, for planar graphs with large girth. In each case, we consider the smallest target graph such that the corresponding homomorphism is NP-complete. These target graphs T4, T5, and T6 have 4, 5, and 6 vertices, respectively. For i ∈ {4, 5, 6} and for every g, w...

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

Seymour’s Second Neighborhood Conjecture asserts that every oriented graph has a vertex whose first out-neighborhood is at most as large as its second out-neighborhood. We introduce the generalized comb, characterize them and prove that every oriented graph missing it satisfies this conjecture.

The Caccetta-Häggkvist conjecture would determine the minimum outdegree which forces a cycle of length at most k in an oriented graph. We study the related question of which minimum outand indegree forces a cycle of length exactly k in an oriented graph. We answer this question whenever k is not a multiple of 3 and propose a conjecture for the other cases.

A famous conjecture of Gyárfás and Sumner states for any tree T and integer k, if the chromatic number of a graph is large enough, either the graph contains a clique of size k or it contains T as an induced subgraph. We discuss some results and open problems about extensions of this conjecture to oriented graphs. We conjecture that for every oriented star S and integer k, if the chromatic numbe...

In 1880, P. G. Tait showed that the four colour theorem is equivalent to the assertion that every 3-regular planar graph without cut-edges is 3-edge-colourable, and in 1891, J. Petersen proved that every 3-regular graph with at most two cut-edges has a 1-factor. In this paper, we introduce the notion of collapsing all edges of a 1-factor of a 3-regular planar graph, thereby obtaining what we ca...

For this paper, we will define a (non-oriented) graph Γ to be a pair Γ = (V,E), where V = vert(Γ) is a set of vertices, and E = edge(Γ) ⊆ V × V/S2 is a set of unordered pairs, known as edges between them. Two vertices, v, v′ ∈ V are considered adjacent if (v, v′) ∈ E, if there is an edge between them. An oriented graph has edge set E = edge(Γ) ⊆ V × V , ordered pairs. For an edge v = (v1, v2) i...

An oriented graph is 2-stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let H be a 2-stratified oriented graph rooted at some blue vertex. An H-coloring of an oriented graph D is a red-blue coloring of the vertices of D in which every blue vertex v belongs to a copy of H rooted at v in D....