Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949837 | Discrete Applied Mathematics | 2017 | 13 Pages |
Abstract
Let D be a strongly connected directed graph of order nâ¥4. In Bang-Jensen et al. (1996), (J. of Graph Theory 22 (2) (1996) 181-187), J. Bang-Jensen, G. Gutin and H. Li proved the following theorems: If (â)d(x)+d(y)â¥2nâ1 and min{d(x),d(y)}â¥nâ1 for every pair of non-adjacent vertices x,y with a common in-neighbour or (ââ)min{d+(x)+dâ(y),dâ(x)+d+(y)}â¥n for every pair of non-adjacent vertices x,y with a common in-neighbour or a common out-neighbour, then D is Hamiltonian. In this paper we show that: (i) if D satisfies condition (â) and the minimum semi-degree of D at least two or (ii) if D is not directed cycle and satisfies condition (ââ), then either D contains a cycle of length nâ1 or n is even and D is isomorphic to the complete bipartite digraph or to the complete bipartite digraph minus one arc.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
S.Kh. Darbinyan, I.A. Karapetyan,