随机图的交叉数与应力
Crossing Numbers and Stress of Random Graphs
摘要：
考虑$\mathbb{R}^d$中随机点过程上的随机几何图。当且仅当两点的距离由指定的距离参数限定时，两点通过边连接。我们表明，投影到一个二维的平面上的图形预计会产生一个常数因子交叉数（和直线交叉数）近似。我们还表明，交叉数呈正相关的图形的投影的应力。
英文摘要：
Consider a random geometric graph over a random point process in $\mathbb{R}^d$. Two points are connected by an edge if and only if their distance is bounded by a prescribed distance parameter. We show that projecting the graph onto a two dimensional plane is expected to yield a constant-factor crossing number (and rectilinear crossing number) approximation. We also show that the crossing number is positively correlated to the stress of the graph's projection.
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。
