@article{oai:u-ryukyu.repo.nii.ac.jp:02000879,
 author = {Maehara, Hiroshi},
 issue = {6},
 journal = {European Journal of Combinatorics},
 month = {Aug},
 note = {Let $S^d$ denote a unit sphere in the $(d+1)$-dimensional Euclidean space $\bold R^{d+1} (d\geq 1)$. For a simple graph $G_{\scr E}$ with edge set $\scr E$, take independent random points $x_k, k\in V(G_{\scr E})$, on $S^d$, and let $D_{\scr E}$ be the minimum value of the spherical distance between $x_i,x_j$ for $\{i,j\}\in\scr E$. We prove that $, \scr E, D^d_{\scr E}$ is asymptotically (as $, \scr E, \to\infty$) distributed to the exponential distribution with mean $dB(\frac 12,\frac d2)$, where $B(p,q)$ is the beta function., 論文},
 pages = {713--717},
 title = {The length of the shortest edge of a graph on a sphere},
 volume = {23},
 year = {2002}
}