Planar Turán Numbers of Cycles: A Counterexample
Date
2021-10-05
Authors
Cranston, Daniel
Lidicky, Bernard
Liu, Xiaonan
Shantanam, Abhinav
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
© Author(s) 2021
Authors
Research Projects
Organizational Units
Organizational Unit
Journal Issue
Is Version Of
Versions
Series
Department
Mathematics
Abstract
The planar Turan number exP(Cℓ,n) is the largest number of edges in an n-vertex planar graph with no ℓ-cycle. For ℓ∈{3,4,5,6}, upper bounds on exP(Cℓ,n) are known that hold with equality infinitely often. Ghosh, Györi, Martin, Paulo, and Xiao [arXiv:2004.14094] conjectured an upper bound on exP(Cℓ,n) for every ℓ≥7 and n sufficiently large. We disprove this conjecture for every ℓ≥11. We also propose two revised versions of the conjecture.
Comments
This preprint is made available through arXiv:https://arxiv.org/abs/2110.02043.
This work is licensed under the Creative Commons Attribution 4.0 License.