The vertex set and arc set of a digraph D are denoted by V (D) and E (D), respectively, and the number of vertices in a digraph D is denoted by n (D). A directed cycle (path, walk) in a digraph will simply be called a cycle (path, walk). A graph or digraph is called hamiltonian if it contains a cycle that visits every vertex, traceable if it contains a path that visits every vertex, and walkabl...

We introduce a decomposition scheme for abstract dialectical frameworks (ADFs). The decomposition proceeds along the ADF’s strongly connected components. For several semantics, the decomposition-based version coincides with the original semantics. For others, the scheme defines new semantics. These new semantics allow us to deal with pertinent problems such as odd-length negative cycles in a mo...

In this paper we characterize the automorphisms (collineations) of the Segre product of partial linear spaces. In particular, we show that if all components of the product are strongly connected, then every collineation is determined by a set of isomorphisms between its components. The formalization follows the ideas presented in the Journal of Geometry paper [16] by Naumowicz and Prażmowski.

In this paper, we determine some limit distributions of pattern statistics in rational stochastic models. We present a general approach to analyze these statistics in rational models having an arbitrary number of strongly connected components. We explicitly establish the limit distributions in most significant cases; they are characterized by a family of unimodal density functions defined by me...

Given a directed graph G, the K node-disjoint paths problem consists in finding a partition of G into K node-disjoint paths, such that each path ends up in a given subset of nodes in G. This article provides a necessary condition for the K node-disjoint paths problem which combines (1) the structure of the reduced graph associated with G, (2) the structure of each strongly connected component o...

In the context of the degree/diameter problem for directed graphs, it is known that the number of vertices of a strongly connected bipartite digraph satisfies a Moore-like bound in terms of its diameter k and the maximum out-degrees (d1; d2) of its partite sets of vertices. It has been proved that, when d1d2 > 1, the digraphs attaining such a bound, called Moore bipartite digraphs, only exist w...

William F. Klostermeyer Dept. Statistics and Computer Science West Virginia University Morgantown, WV 26506-6330 e-mail: [email protected] ABSTRACT A directed graph operation called pushing a vertex is studied. When a vertex is pushed, the orientation of each of its incident edges is reversed. We consider the problems of pushing vertices so as to produce strongly connected, semi-connected, and acy...

Lower Bound. Adrian Vetta Abstract We present a 32 -approximation algorithm for the problem of nding a minimum strongly connected spanning subgraph in a given directed graph. As a corollary we obtain a 3 2 -approximation algorithm for the more general minimum equivalent digraph problem. The performance of our algorithm is measured against a lower bound obtained from a simple matching problem. T...

Abstract The global dynamics of the two-species Lotka–Volterra competition patch model with asymmetric dispersal is classified under assumptions that weak and weighted digraph connection matrix strongly connected cycle-balanced. We show in long time, either exclusion holds one species becomes extinct, or two reach a coexistence equilibrium, outcome determined by strength inter-specific rates. O...