Graphs and Combinatorics

, Volume 13, Issue 3, pp 267–273 | Cite as

On a Conjecture on Directed Cycles in a Directed Bipartite Graph

  • Charles Little
  • Kee Teo
  • Hong Wang


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 xV 1 and yV 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].


Bipartite Graph Directed Graph Discrete Math Hamilton Cycle Hamilton Path 
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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Charles Little
    • 1
  • Kee Teo
    • 1
  • Hong Wang
    • 2
  1. 1.Department of MathematicsMassey UniversityPalmerston NorthNew Zealand
  2. 2.Department of MathematicsUniversity of New OrleansNew OrleansUSA

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