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Creators/Authors contains: "Cranston, Daniel W"

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  1. ; (, SIAM Journal on Discrete Mathematics)
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  2. ; ; ; (, The Electronic Journal of Combinatorics)
    The planar Turán number $$\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$$ is the largest number of edges in an $$n$$-vertex planar graph with no $$\ell$$-cycle. For each $$\ell\in \{3,4,5,6\}$$, upper bounds on $$\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$$ are known that hold with equality infinitely often. Ghosh, Győri, Martin, Paulos, and Xiao [arXiv:2004.14094] conjectured an upper bound on $$\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$$ for every $$\ell\ge 7$$ and $$n$$ sufficiently large. We disprove this conjecture for every $$\ell\ge 11$$. We also propose two revised versions of the conjecture. 
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