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On a Conjecture on Directed Cycles in a Directed Bipartite Graph

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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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Authors and Affiliations

  1. Department of Mathematics, Massey University, Palmerston North, New Zealand

    Charles Little & Kee Teo

  2. Department of Mathematics, University of New Orleans, New Orleans, LA, 70148, USA

    Hong Wang

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  1. Charles Little
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  2. Kee Teo
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  3. Hong Wang
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Little, C., Teo, K. & Wang, H. On a Conjecture on Directed Cycles in a Directed Bipartite Graph. Graphs and Combinatorics 13, 267–273 (1997). https://doi.org/10.1007/BF03353004

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  • DOI: https://doi.org/10.1007/BF03353004

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