A characterization is given for acyclic digraphs that are the acyclic intersection digraphs of subpaths of a directed tree.

We resolve two problems of [Cameron, Praeger, and Wormald – Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica 1993]. First, we construct a locally finite highly arc-transitive digraph with universal reachability relation. Second, we provide constructions of 2-ended highly arc transitive digraphs where each ‘building block’ is a finite bipartite graph that is...

I present an algorithm that, given a number $n \geq 1$, computes a compact representation of the set of all noncrossing acyclic digraphs with $n$ nodes. This compact representation can be used as the basis for a wide range of dynamic programming algorithms on these graphs. As an illustration, along with this note I am releasing the implementation of an algorithm for counting the number of noncr...

A digraph with maximum out-degree d and radius k has at most 1+d+ · · ·+d vertices, as the Moore bound states. Regular digraphs attaining such a bound and whose diameter is at most k + 1 are called radially Moore digraphs. Knor [4] proved that these extremal digraphs do exist for any value of d ≥ 1 and k ≥ 1. In this paper, we introduce a digraph operator, based on the line digraph, which allow...

Kautz digraphs K(d, `) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d, `) were recently introduced by Böhmová, Huemer and the author, and some of its distance-related parameters were fixed. In this paper we propose a new approach to cyclic Kautz digraphs by introducing the family ...

Given a digraph D and a subset X of vertices of D, pushing X in D means reversing the orientation of all arcs with exactly one end in X. It is known that the problem of deciding whether a given digraph can be made acyclic using the push operation is NP-complete for general digraphs, and polynomial time solvable for multipartite tournaments. Here, we continue the study of deciding whether a digr...

In this paper, we study two types of strong subgraph packing problems in digraphs, including internally disjoint problem and arc-disjoint problem. These can be viewed as generalizations the famous Steiner tree are closely related to arc decomposition We first prove NP-completeness for restricted symmetric digraphs Eulerian digraphs. Then get inapproximability results Finally digraph composition...

We prove that every digraph of circumference l has DAG-width at most l and this is best possible. As a consequence of our result we deduce that the k-linkage problem is polynomially solvable for every fixed k in the class of digraphs with bounded circumference. This answers a question posed in [2]. We also prove that the weak k-linkage problem (where we ask for arc-disjoint paths) is polynomial...

A digraph G is a difference digraph iff there exists an S ⊂ IN such that G is isomorphic to the digraph DD(S) = (V,A), where V = S and A = {(i, j) : i, j ∈ V ∧ i− j ∈ V }. For some classes of digraphs, e.g. alternating trees, oriented cycles, tournaments etc., it is known, under which conditions these digraphs are difference digraphs (cf. [5]). We generalize the so-called sourcejoin (a construc...