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.
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Aldred, R.E.L., Holton, D.A. Cycles through five edges in 3-connected cubic graphs. Graphs and Combinatorics 3, 299–311 (1987). https://doi.org/10.1007/BF01788553
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DOI: https://doi.org/10.1007/BF01788553