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Title:
On pre-Hamiltonian Cycles in Balanced Bipartite Digraphs
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Uncontrolled Keywords:
Digraphs ; Cycles ; Hamiltonian cycles ; Bipartite balanced digraph ; Pancyclic
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Abstract:
Let D be a strongly connected balanced bipartite directed graph of order 2a ≥ 10. Let x, y be distinct vertices in D. {x,y} dominates a vertex z if x → z and y → z; in this case, we call the pair {x,y} dominating. In this paper we prove: If max{d(x); d(y)} ≥ 2a-2 for every dominating pair of vertices {x,y} then either the underlying graph of D is 2-connected or D contains a cycle of length 2a - 2 or D is isomorphic to one digraph of order ten.