منابع مشابه
The consecutive-4 digraphs are Hamiltonian
Du, Hsu, and Hwang conjectured that consecutive-d digraphs are Hamiltonian for d = 3, 4. Recently, we gave an infinite class of consecutive-3 digraphs, which are not Hamiltonian. In this article we prove the conjecture for d = 4. c © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 1–6, 1999
متن کاملOn connectivity of consecutive-d digraphs
The concept of a consecutive-d digraph was proposed by Du, Hsu and Hwang as a generalization of de Bruijn digraphs, Kautz digraphs, and their generalizations given by Imase and Itoh and Reddy, Pradhan and Kuhl. In this paper we determine the connectivity of consecutive-d digraphs and study how to modify consecutive-d digraphs to reach maximum connectivity. Our results will generalize and improv...
متن کاملRemarks on hamiltonian digraphs
An oriented graph is an out-tournament if the out-neighbourhood of every vertex is a tournament. This note is motivated by A. Kemnitz and B. Greger, Congr. Numer. 130 (1998) 127-131. We show that the main result of the paper by Kemnitz and Greger is an easy consequence of the characterization of hamiltonian out-tournaments by Bang-Jensen, Huang and Prisner, J. Combin. Theory Ser. B 59 (1993) 26...
متن کاملOn endo-Cayley digraphs: The hamiltonian property
Given a finite abelian group A, a subset ⊆ A and an endomorphism of A, the endo-Cayley digraph GA( , ) is defined by taking A as the vertex set and making every vertex x adjacent to the vertices (x)+ a with a ∈ . When A is cyclic and the set is of the form = {e, e + h, . . . , e + (d − 1)h}, the digraph G is called a consecutive digraph. In this paper we study the hamiltonicity of endo-Cayley d...
متن کاملHamiltonian degree sequences in digraphs
We show that for each η > 0 every digraph G of sufficiently large order n is Hamiltonian if its outand indegree sequences d+1 ≤ · · · ≤ d + n and d−1 ≤ · · · ≤ d − n satisfy (i) d + i ≥ i+ ηn or d − n−i−ηn ≥ n− i and (ii) d − i ≥ i+ ηn or d+n−i−ηn ≥ n− i for all i < n/2. This gives an approximate solution to a problem of Nash-Williams [22] concerning a digraph analogue of Chvátal’s theorem. In ...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1989
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-25-1-47-55