7 research outputs found
A new sufficient condition for a 2-strong digraph to be Hamiltonian
In this paper we prove the following new sufficient condition for a digraph
to be Hamiltonian:
{\it Let be a 2-strong digraph of order .
If vertices of have degrees at least and the remaining vertex
has degree at least , where is a non-negative integer, then is
Hamiltonian}.
This is an extension of Ghouila-Houri's theorem for 2-strong digraphs and is
a generalization of an early result of the author (DAN Arm. SSR (91(2):6-8,
1990). The obtained result is best possible in the sense that for there
is a digraph of order (respectively, ) with the minimum degree
(respectively, with the minimum ) whose vertices have
degrees at least , but it is not Hamiltonian.
We also give a new sufficient condition for a 3-strong digraph to be
Hamiltonian-connected.Comment: 20 pages, 2 figure