# Bridged Hamiltonian Cycles in Sub-critical Random Geometric Graphs

@article{Ganesan2021BridgedHC,
title={Bridged Hamiltonian Cycles in Sub-critical Random Geometric Graphs},
author={Ghurumuruhan Ganesan},
journal={Sankhya A},
year={2021}
}
In this paper, we consider a random geometric graph (RGG) G on n nodes with adjacency distance rn just below the Hamiltonicity threshold and construct Hamiltonian cycles using additional edges called bridges. The bridges by definition do not belong to G and we are interested in estimating the number of bridges and the maximum bridge length, needed for constructing a Hamiltonian cycle. In our main result, we show that with high probability, i.e. with probability converging to one as n → ∞, we…

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