Co-author(s) :

Karapetyan Iskandar

Abstract:

Let D be a strongly connected directed graph of order n≥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 (∗)d(x)+d(y)≥2n−1 and min{d(x),d(y)}≥n−1 for every pair of non-adjacent vertices x,y with a common in-neighbour or (∗∗)min{d+(x)+d−(y),d−(x)+d+(y)}≥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 (∗) and the minimum semi-degree of D at least two or (ii) if D is not directed cycle and satisfies condition (∗∗), then either D contains a cycle of length n−1 or n is even and D is isomorphic to the complete bipartite digraph or to the complete bipartite digraph minus one arc.

Publisher:

Elsevier

Date submitted:

16.04.2015

Date accepted:

03.02.2016

Date of publication:

15.03.2016

Identifier:

oai:noad.sci.am:136097

DOI:

10.1016/j.dam.2016.02.010

ISSN:

0166-218X

Language:

English

Journal or Publication Title:

Discrete Applied Mathematics

Volume:

216

Number:

3

URL:

Additional Information:

samdarbin@ipia.sci.am ; isko@ipia.sci.am

Affiliation:

Institute for Informatics and Automation Problems

Country:

Armenia

Indexing:

WOS