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On a question of van Aardt et al. on destroying all longest cycles

(2019) GRAPHS AND COMBINATORICS. 35(2). p.479-483
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Abstract
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.
Keywords
Longest cycle, Circumference, Vertex deletion, SUBGRAPH

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Please use this url to cite or link to this publication:

Chicago
Zamfirescu, Carol. 2019. “On a Question of Van Aardt Et Al. on Destroying All Longest Cycles.” Graphs and Combinatorics 35 (2): 479–483.
APA
Zamfirescu, C. (2019). On a question of van Aardt et al. on destroying all longest cycles. GRAPHS AND COMBINATORICS, 35(2), 479–483.
Vancouver
1.
Zamfirescu C. On a question of van Aardt et al. on destroying all longest cycles. GRAPHS AND COMBINATORICS. 2019;35(2):479–83.
MLA
Zamfirescu, Carol. “On a Question of Van Aardt Et Al. on Destroying All Longest Cycles.” GRAPHS AND COMBINATORICS 35.2 (2019): 479–483. Print.
@article{8603334,
  abstract     = {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.},
  author       = {Zamfirescu, Carol},
  issn         = {0911-0119},
  journal      = {GRAPHS AND COMBINATORICS},
  keywords     = {Longest cycle,Circumference,Vertex deletion,SUBGRAPH},
  language     = {eng},
  number       = {2},
  pages        = {479--483},
  title        = {On a question of van Aardt et al. on destroying all longest cycles},
  url          = {http://dx.doi.org/10.1007/s00373-019-02010-9},
  volume       = {35},
  year         = {2019},
}

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