HAMILTON CYCLES IN RANDOM GEOMETRIC GRAPHS

被引：23

作者：

Balogh, Jozsef ^{[1
]}

Bollobas, Bela ^{[3
]}

Krivelevich, Michael ^{[2
]}

Muller, Tobias ^{[4
]}

Walters, Mark ^{[5
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Tel Aviv Univ, Sch Math Sci, IL-69978 Tel Aviv, Israel

[3] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England

[4] Ctr Wiskunde & Informat, NL-1090 GB Amsterdam, Netherlands

[5] Univ London, Sch Math Sci, London E1 4NS, England

来源：

ANNALS OF APPLIED PROBABILITY | 2011年 / 21卷 / 03期

基金：

美国国家科学基金会; 以色列科学基金会;

关键词：

Hamilton cycles; random geometric graphs; CONNECTIVITY;

D O I：

10.1214/10-AAP718

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penrose. We also show that in the k-nearest neighbor model, there is a constant. such that almost every kappa-connected graph has a Hamilton cycle.

引用

页码：1053 / 1072

页数：20

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