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- W4387561330 abstract "The $textit{planar Tur'an number}$ $textrm{ex}_{mathcal P}(n,H)$ of a graph $H$ is the maximum number of edges in an $n$-vertex planar graph without $H$ as a subgraph. Let $C_k$ denote the cycle of length $k$. The planar Tur'an number $textrm{ex}_{mathcal P}(n,C_k)$ is known for $kle 7$. We show that dense planar graphs with a certain connectivity property (known as circuit graphs) contain large near triangulations, and we use this result to obtain consequences for planar Tur'an numbers. In particular, we prove that there is a constant $D$ so that $textrm{ex}_{mathcal P}(n,C_k) le 3n - 6 - Dn/k^{log_2^3}$ for all $k, nge 4$. When $k ge 11$ this bound is tight up to the constant $D$ and proves a conjecture of Cranston, Lidick'y, Liu, and Shantanam." @default.
- W4387561330 created "2023-10-12" @default.
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- W4387561330 date "2023-10-10" @default.
- W4387561330 modified "2023-10-13" @default.
- W4387561330 title "Dense circuit graphs and the planar Tur'an number of a cycle" @default.
- W4387561330 doi "https://doi.org/10.48550/arxiv.2310.06631" @default.
- W4387561330 hasPublicationYear "2023" @default.
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