Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamilton cycles in random geometric graphs   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 \kappa\ such that almost every \kappa-connected
graph has a Hamilton cycle.

19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
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The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga