AI 中文总结
研究无\(C_8\)的\(n\)顶点简单平面图边数上界，通过证明得到改进后的上界公式，为该领域研究提供了更优结果。
AI 中文摘要
我们证明，对于每个\(n\geq8\)的无\(C_8\)的\(n\)顶点简单平面图，其边数至多为\(\frac{69}{25}(n - 2)\)。这改进了对于每个\(n\geq27\)时已知的最佳界\(\frac{323}{108}n - 6\)。
英文摘要
We prove that every $n$-vertex simple planar graph with no copy of $C_8$ has at most \[ \frac{69}{25}(n-2) \] edges, for every $n\ge 8$. This improves the best known bound \[ \frac{323}{108}n-6 \qquad \text{for every } n\ge 27. \]
CommentsThe main paper is 8 pages long, with a 16-page appendix
