On a Question of van Aardt et al. on Destroying All Longest Cycles
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We describe an infinite family of 2-connected graphs, each of which has the property that the intersection of all longest cycles is empty. In particular, we present such graphs with circumference 10, 13, and 16. This settles a question of van Aardt et al. (Discrete Appl Math 186:251–259, 2015) concerning the existence of such graphs for all but one case, namely circumference 11. We also present a 2-connected graph of circumference 11 in which all but one vertex are avoided by some longest cycle.
KeywordsLongest cycle Circumference Vertex deletion
Mathematics Subject Classification05C38
This research was supported by a Postdoctoral Fellowship of the Research Foundation Flanders (FWO).
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