Name
Abstract | ||
|---|---|---|
The planar Turan 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 $\ell\in \{3,4,5,6\}$, upper bounds on $\textrm{ex}_{\mathcal{P}}(C_{\ell},n)$ are known that hold with equality infinitely often. Ghosh, Gy\"{o}ri, Martin, Paulo, 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. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.37236/10774 | The Electronic Journal of Combinatorics |
DocType | Volume | Issue |
Journal | 29 | 3 |
ISSN | Citations | PageRank |
1077-8926 | 0 | 0.34 |
References | Authors | |
0 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel W. Cranston | 1 | 0 | 0.34 |
| Bernard Lidický | 2 | 9 | 5.00 |
| Xiaonan Liu | 3 | 1 | 1.70 |
| Abhinav Shantanam | 4 | 0 | 0.34 |