منابع مشابه
On k-strong and k-cyclic digraphs
Thomassen proved that there is no degree of strong connectivity which guarantees a cycle through two given vertices in a digraph (Combinatorica 11 (1991) 393-395). In this paper we consider a large family of digraphs, including symmetric digraphs (i.e. digraphs obtained from undirected graphs by replacing each edge by a directed cycle of length two), semicomplete bipartite digraphs, locally sem...
متن کاملON k-STRONG DISTANCE IN STRONG DIGRAPHS
For a nonempty set S of vertices in a strong digraph D, the strong distance d(S) is the minimum size of a strong subdigraph of D containing the vertices of S. If S contains k vertices, then d(S) is referred to as the k-strong distance of S. For an integer k > 2 and a vertex v of a strong digraph D, the k-strong eccentricity sek(v) of v is the maximum k-strong distance d(S) among all sets S of k...
متن کامل1)-KERNELS IN STRONG k-TRANSITIVE DIGRAPHS
Let D = (V (D), A(D)) be a digraph and k ≥ 2 be an integer. A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N , we have d(u, v) ≥ k; it is l-absorbent if for every u ∈ V (D)−N , there exists v ∈ N such that d(u, v) ≤ l. A (k, l)-kernel of D is a k-independent and l-absorbent subset of V (D). A k-kernel is a (k, k − 1)-kernel. A digraphD is k-transitive if for any path ...
متن کاملOn the structure of strong k-transitive digraphs
A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work...
متن کاملCyclically k-partite digraphs and k-kernels
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 set of vertices (if u, v ∈ N 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). A k-kernel is a (k, k − 1)-kernel. A digraph D is cyclically k-partite if there exists a partition {Vi} i=0 of V (D) suc...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00300-l