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 ...

Entanglement is a complexity measure of digraphs that origins in fixedpoint logics. Its combinatorial purpose is to measure the nested depth of cycles in digraphs. We address the problem of characterizing the structure of graphs of entanglement at most k. Only partial results are known so far: digraphs for k = 1, and undirected graphs for k = 2. In this paper we investigate the structure of und...

Given a digraph (an undirected graph, resp.) D and two positive integers f (x); g(x) for every x 2 V (D), a subgraph H of D is called a (g; f)-factor if g(x) d + H (x) = d ? H (x) f (x)(g(x) d H (x) f (x), resp.) for every x 2 V (D). If f (x) = g(x) = 1 for every x, then a connected (g; f)-factor is a hamiltonian cycle. The previous research related to the topic has been carried out either for ...

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...

In this paper we investigate new sufficient conditions for a digraph to be kernel-perfect (KP) and some structural properties of kernel-perfect critical (KPC) digraphs. In particular, it is proved that the asymmetrical part of any KPC digraph is strongly connected. A new method to construct KPC digraphs is developed. The existence of KP and KPC digraphs with arbitrarily large dichromatic number...