@article{oai:u-ryukyu.repo.nii.ac.jp:02000876,
 author = {Maehara, Hiroshi},
 issue = {5},
 journal = {European Journal of Combinatorics},
 month = {Jul},
 note = {Drop $N$ spherical caps, each of area $4\pi ･ $p(N)$, at random on the surface of a unit sphere, and let $G\sb{p}$  denote the intersection graphs of these random caps. Among others, we prove the following: (1) If $N(N\sb{p})\sp{n-1}\to\0$ as $N \to\infty$, then ${\rm Pr}(G\sb{p}\text{ has no component of order }\geq n)\to1$, while if $N(N\sb{p})\sp(n-1) \to\ infty$ then ${\rm Pr}(G\sb{p}\text{ has an $n$-clique})\to1$ as $N\to\infty$. (2) If, $p<(1-\varepsilon)\log N/4N$, $\varepsilon>0$ then ${\rm Pr}(\delta=0)\to1$, while if $p>(1+\varepsilon)\log N/4N$ then for any positive integer $n$, ${\rm Pr}(\delta\geq n)\to1$ as $ N\to\infty$, where $\delta$ denotes the minimum degree of $G\sb{p}$. (3) If $p=(\log N+x)/4N$ then the number of isolated vertices of $G\sb{p}$ is asymptotically $(N\to\infty)$ distributed according to Poisson distribution with mean $e\sp{-x}$. (4) If $p>(1+\varepsilon)\log N/2N$, then ${\rm Pr}(G\sb{p}\text{ is $2$-connected})\to 1$ as $N\to\infty$., 論文},
 pages = {707--718},
 title = {On the intersection graph of random caps on a sphere},
 volume = {25},
 year = {2004}
}