منابع مشابه
quasi - transitive digraphs ∗
Let D = (V , A) be a directed graph (digraph) without loops nor multiple arcs. A set of vertices S of a digraph D is a (k, l)-kernel of D if and only if for any two vertices u, v in S, d(u, v) ≥ k and for any vertex u in V \ S there exists v in S such that d(u, v) ≤ l. A digraph D is called quasi-transitive if and only if for any distinct vertices u, v, w of D such that u→ v → w, then u and w a...
متن کاملKernels in quasi-transitive digraphs
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs
متن کاملOn the existence and number of (k+1)-kings in k-quasi-transitive digraphs
Let D = (V (D), A(D)) be a digraph and k ≥ 2 an integer. We say that D is k-quasi-transitive if for every directed path (v0, v1, . . . , vk) in D, then (v0, vk) ∈ A(D) or (vk, v0) ∈ A(D). Clearly, a 2-quasi-transitive digraph is a quasi-transitive digraph in the usual sense. Bang-Jensen and Gutin proved that a quasi-transitive digraph D has a 3king if and only if D has a unique initial strong c...
متن کاملMinimum cycle factors in quasi-transitive digraphs
We consider the minimum cycle factor problem: given a digraph D, find the minimum number kmin(D) of vertex disjoint cycles covering all vertices of D or verify that D has no cycle factor. There is an analogous problem for paths, known as the minimum path factor problem. Both problems are NP-hard for general digraphs as they include the Hamilton cycle and path problems, respectively. In 1994 Gut...
متن کاملK-kernels in K-transitive and K-quasi-transitive Digraphs
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 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. A digraph D is transitive if (u, v), (v, w) ∈ A(D) implies that (u,w) ∈ A(D). This co...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00179-9