几何Johnson图的连通性和直径
On the Connectedness and Diameter of a Geometric Johnson Graph
摘要：
设$P$是平面中一般位置上的一组$n$点。如果存在一个凸集$C$使得$I = P \cap C$，则称$P$的子集$I$为\emph{island}。本文定义了$P$的\emph{generalized island Johnson graph}为这样的图，其顶点由$k$的所有$P$的岛组成，其中两个岛相邻，如果它们的交集恰好由$l$元素组成。我们证明了，对于足够大的值的$n$，这个图是连通的，并给出了其直径的上限和下界。
英文摘要：
Let $P$ be a set of $n$ points in general position in the plane. A subset $I$ of $P$ is called an \emph{island} if there exists a convex set $C$ such that $I = P \cap C$. In this paper we define the \emph{generalized island Johnson graph} of $P$ as the graph whose vertex consists of all islands of $P$ of cardinality $k$, two of which are adjacent if their intersection consists of exactly $l$ elements. We show that for large enough values of $n$, this graph is connected, and give upper and lower bounds on its diameter.
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。
