53 research outputs found
A Note on Long non-Hamiltonian Cycles in One Class of Digraphs
Let be a strong digraph on vertices. In [3, Discrete Applied
Math., 95 (1999) 77-87)], J. Bang-Jensen, Y. Guo and A. Yeo proved the
following theorem: if (*) and for every pair of non-adjacent vertices
with a common in-neighbour or a common out-neighbour, then is hamiltonian.
In this note we show that: if is not directed cycle and satisfies the
condition (*), then contains a cycle of length or .Comment: 7 pages. arXiv admin note: substantial text overlap with
arXiv:1207.564
A sufficient condition for a balanced bipartite digraph to be hamiltonian
We describe a new type of sufficient condition for a balanced bipartite
digraph to be hamiltonian. Let be a balanced bipartite digraph and be
distinct vertices in . dominates a vertex if
and ; in this case, we call the pair dominating. In
this paper, we prove that a strong balanced bipartite digraph on
vertices contains a hamiltonian cycle if, for every dominating pair of vertices
, either and or and
. The lower bound in the result is sharp.Comment: 12 pages, 3 figure
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