Graphs and Combinatorics

, Volume 3, Issue 1, pp 299–311

Cycles through five edges in 3-connected cubic graphs

• R. E. L. Aldred
• D. A. Holton
Article

Abstract

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.

Keywords

Obvious Reason Suitable Restriction Cycle Passing
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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