Graphs and Combinatorics

, Volume 35, Issue 2, pp 479–483 | Cite as

On a Question of van Aardt et al. on Destroying All Longest Cycles

  • Carol T. ZamfirescuEmail author
Original Paper


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.


Longest cycle Circumference Vertex deletion 

Mathematics Subject Classification




This research was supported by a Postdoctoral Fellowship of the Research Foundation Flanders (FWO).


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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Computer Science and StatisticsGhent UniversityGhentBelgium
  2. 2.Department of MathematicsBabeş-Bolyai UniversityCluj-NapocaRomania

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