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On the intersection graph of random caps on a sphere
http://hdl.handle.net/20.500.12000/149
http://hdl.handle.net/20.500.12000/14983f8008e-8f10-4b55-a306-1e2ec53af407
名前 / ファイル | ライセンス | アクション |
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maehara_h01.pdf
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Item type | デフォルトアイテムタイプ(フル)(1) | |||||||
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公開日 | 2007-03-01 | |||||||
タイトル | ||||||||
タイトル | On the intersection graph of random caps on a sphere | |||||||
言語 | en | |||||||
作成者 |
Maehara, Hiroshi
× Maehara, Hiroshi
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アクセス権 | ||||||||
アクセス権 | open access | |||||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||
内容記述 | ||||||||
内容記述タイプ | Other | |||||||
内容記述 | 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 $N\to\infty$. | |||||||
内容記述 | ||||||||
内容記述タイプ | Other | |||||||
内容記述 | 論文 | |||||||
出版者 | ||||||||
言語 | en | |||||||
出版者 | Elsevier Science B.V., Amsterdam | |||||||
言語 | ||||||||
言語 | eng | |||||||
資源タイプ | ||||||||
資源タイプ | journal article | |||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
出版タイプ | ||||||||
出版タイプ | AM | |||||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||
識別子 | ||||||||
識別子 | http://hdl.handle.net/20.500.12000/149 | |||||||
識別子タイプ | HDL | |||||||
関連情報 | ||||||||
識別子タイプ | URI | |||||||
関連識別子 | http://www.sciencedirect.com/science/journal/01956698 | |||||||
関連情報 | ||||||||
識別子タイプ | DOI | |||||||
関連識別子 | 10.1016/j.ejc.2003.10.005 | |||||||
収録物識別子 | ||||||||
収録物識別子タイプ | ISSN | |||||||
収録物識別子 | 01956698 | |||||||
収録物識別子 | ||||||||
収録物識別子タイプ | NCID | |||||||
収録物識別子 | AA00181294 | |||||||
収録物名 | ||||||||
言語 | en | |||||||
収録物名 | European Journal of Combinatorics | |||||||
書誌情報 |
巻 25, 号 5, p. 707-718, 発行日 2004-07 |