Hamilton Cycles in Random Geometric Graphs

Details Hamilton Cycles in Random Geometric Graphs Hamilton Cycles in Random Geometric Graphs

2009-05-28

arxiv.org/abs/0905.4650v1

Mathematics

Probability

Scientific paper

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
$\kappa$ such that almost every $\kappa$-connected graph has a Hamilton cycle.

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