论文标题
极端平面图，没有特定长度的周期
Extremal planar graphs with no cycles of particular lengths
论文作者
论文摘要
在本文中，我们估算了某些图的平面Turán数字$ \ MATHRM {ex} _ \ MATHCAL {p}（n，h）$，即$ h $，即平面图$ g $ of $ n $ vertices中不包含$ h $的最大边缘数量。当$ h = C_5 $时，我们给出了一个新的，简短的证明，并在$ g $不合时宜或不含三角形的情况下研究案例，而$ h $是一个短的偶数周期。证明主要是Ghosh，Győri，Martin，Paulos和Xiao在Arxiv中引入的“贡献方法”的新应用或变体：2004.14094。
In this paper we estimate the planar Turán number $\mathrm{ex}_\mathcal{P}(n,H)$ of some graphs $H$, i.e., the maximum number of edges in a planar graph $G$ of $n$ vertices not containing $H$ as a subgraph. We give a new, short proof when $H=C_5$, and study the cases when $G$ is bipartite or triangle-free and $H$ is a short even cycle. The proofs are mostly new applications or variants of the "contribution method" introduced by Ghosh, Győri, Martin, Paulos and Xiao in arXiv:2004.14094.
