Displaying similar documents to “Reachability relations and the structure of transitive digraphs.”

4-Transitive Digraphs I: The Structure of Strong 4-Transitive Digraphs

César Hernández-Cruz (2013)

Discussiones Mathematicae Graph Theory

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Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices u, v,w ∈ V (D), (u, v), (v,w) ∈ A(D) implies that (u,w) ∈ A(D). This concept can be generalized as follows: A digraph is k-transitive if for every u, v ∈ V (D), the existence of a uv-directed path of length k in D implies that (u, v) ∈ A(D). A very useful structural characterization of transitive digraphs has been known for a...

On the Existence of (k,l)-Kernels in Infinite Digraphs: A Survey

H. Galeana-Sánchez, C. Hernández-Cruz (2014)

Discussiones Mathematicae Graph Theory

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Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N, u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k −1)-kernel. This work is a survey of results proving sufficient conditions for the existence of (k, l)-kernels in infinite digraphs. Despite all the previous work in this direction...

k-Kernels and some operations in digraphs

Hortensia Galeana-Sanchez, Laura Pastrana (2009)

Discussiones Mathematicae Graph Theory

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Let D be a digraph. V(D) denotes the set of vertices of D; a set N ⊆ V(D) is said to be a k-kernel of D if it satisfies the following two conditions: for every pair of different vertices u,v ∈ N it holds that every directed path between them has length at least k and for every vertex x ∈ V(D)-N there is a vertex y ∈ N such that there is an xy-directed path of length at most k-1. In this paper, we consider some operations on digraphs and prove the existence of k-kernels in digraphs formed...

3-transitive digraphs

César Hernández-Cruz (2012)

Discussiones Mathematicae Graph Theory

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Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u,v,w,x) of length 3 in D implies the existence of the arc (u,x) ∈ A(D). In this article strong 3-transitive digraphs are characterized and the structure of non-strong 3-transitive digraphs is described. The results are used, e.g., to characterize 3-transitive digraphs that are transitive and to characterize 3-transitive digraphs...