Graphs and Combinatorics

, Volume 3, Issue 1, pp 299–311 | Cite as

Cycles through five edges in 3-connected cubic graphs

  • R. E. L. Aldred
  • D. A. Holton


Given five edges in a 3-connected cubic graph there are obvious reasons why there may not be one cycle passing through all of them. For instance, an odd subset of the edges may form a cutset of the graph. By restricting the sets of five edges in a natural way we are able to give necessary and sufficient conditions for the set to be a subset of edges of some cycle. It follows as a corollary that, under suitable restrictions, any five edges of a cyclically 5-edge connected cubic graph lie on a cycle.


Obvious Reason Suitable Restriction Cycle Passing 


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • R. E. L. Aldred
    • 1
  • D. A. Holton
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand

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