On a Conjecture on Directed Cycles in a Directed Bipartite Graph |
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| Authors: | Charles Little Kee Teo Hong Wang |
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| Institution: | 1. Department of Mathematics, Massey University, Palmerston North, New Zealand
2. Department of Mathematics, University of New Orleans, New Orleans, LA, 70148, USA
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| Abstract: | Let D = (V 1, V 2; A) be a directed bipartite graph with |V 1| = |V 2| = n ≥ 2. Suppose that d D (x) + d D (y) ≥ 3n for all x ∈ V 1 and y ∈ V 2. Then, with one exception, D contains two vertex-disjoint directed cycles of lengths 2n 1 and 2n 2, respectively, for any positive integer partition n = n 1 + n 2. This proves a conjecture proposed in 9]. |
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