(k+1)-kernels and the number of k-kings in k-quasi-transitive digraphs
نویسندگان
چکیده
منابع مشابه
K-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...
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 کاملK-kernels in Generalizations of 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 set of vertices (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). A k-kernel is a (k, k − 1)-kernel. Quasi-transitive, right-pretransitive and left-pretransitive digraphs are g...
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 کاملKernels in quasi-transitive digraphs
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2015
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.08.009