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22nd Cumberland Conference on Combinatorics, Graph Theory and Computing
May 21-23, 2009
Western Kentucky University
Bowling Green, KY, USA

Organizers
Bela Csaba, Chair; Mustafa Atici; Robert Crawford; Claus Ernst; Dominic Lanphier; Attila Por

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Hamilton Cycles in Random Geometric Graphs
by
Jozsef Balogh
U. of Illinois at UC
Coauthors: Bela Bollobas, Mark Walters

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 proves a conjecture of Penrose.

We also show that in the k-nearest neighbour model, there is a constant k such that almost every k-connected graph has a Hamilton cycle.

Date received: April 7, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayq-12.