凸独立点集上几何图的边复杂性
Edge complexity of geometric graphs on convex independent point sets
摘要：
在本文中，我们专注于广义版本的加布里埃尔图称为局部加布里埃尔图（$LGGs$）和单位距离图（$UDGs$）凸独立点集。$UDGs$是$LGGs$的子图。给出了凸独立点集上的$LGGs$有$2n \log n + O(n)$边的一个简单证明.然后证明了凸独立点集上的单位距离图具有$O(n)$边，从而改进了$O(n \log n)$的已知界。
英文摘要：
In this paper, we focus on a generalised version of Gabriel graphs known as Locally Gabriel graphs ($LGGs$) and Unit distance graphs ($UDGs$) on convexly independent point sets. $UDGs$ are sub graphs of $LGGs$. We give a simpler proof for the claim that $LGGs$ on convex independent point sets have $2n \log n + O(n)$ edges. Then we prove that unit distance graphs on convex independent point sets have $O(n)$ edges improving the previous known bound of $O(n \log n)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
