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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
Article
  • 47 Downloads

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 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].

Keywords

Bipartite Graph Directed Graph Discrete Math Hamilton Cycle Hamilton Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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