论文标题
关于平面位置的点集段的段落段的连通性图
On the connectivity of the disjointness graph of segments of point sets in general position in the plane
论文作者
论文摘要
令$ p $是一组$ n \ geq 3 $点在飞机上的总位置。 $ p $的边缘脱节图$ d（p）$是其顶点的图形，其顶点是$ p $中的端点的所有封闭直线段，其中两个在$ d（p）$中相邻，并且仅当它们是分离时。我们表明，$ d（p）$的连接性至少为$ \ binom {\ lfloor \ frac {n-2} {2} {2} \ rfloor} {2}+\ binom {\ binom {\ lceil {\ lceil \ frac \ frac {n-2} {n-2} {2} {2} {2} \ rceil geil geil n $ n $ n $ n $ n $
Let $P$ be a set of $n\geq 3$ points in general position in the plane. The edge disjointness graph $D(P)$ of $P$ is the graph whose vertices are all the closed straight line segments with endpoints in $P$, two of which are adjacent in $D(P)$ if and only if they are disjoint. We show that the connectivity of $D(P)$ is at least $\binom{\lfloor\frac{n-2}{2}\rfloor}{2}+\binom{\lceil\frac{n-2}{2}\rceil}{2}$, and that this bound is tight for each $n\geq 3$.
