Hamilton cycle problem in strong k-quasi-transitive digraphs with large diameter
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...
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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...
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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 ...
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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...
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In this paper, D = (V (D), A(D)) denotes a loopless directed graph (digraph) with at most one arc from u to v for every pair of vertices u and v of V (D). Given a digraph D, we say that D is 3-quasi-transitive if, whenever u → v → w → z in D, then u and z are adjacent. In [3], Bang-Jensen introduced 3-quasi-transitive digraphs and claimed that the only strong 3quasi-transitive digraphs are the ...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2021
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2187