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- W2952165733 abstract "We show for an arbitrary $ell_p$ norm that the property that a random geometric graph $mathcal G(n,r)$ contains a Hamiltonian cycle exhibits a sharp threshold at $r=r(n)=sqrt{frac{log n}{alpha_p n}}$, where $alpha_p$ is the area of the unit disk in the $ell_p$ norm. The proof is constructive and yields a linear time algorithm for finding a Hamiltonian cycle of $RG$ a.a.s., provided $r=r(n)gesqrt{frac{log n}{(alpha_p -epsilon)n}}$ for some fixed $epsilon > 0$." @default.
- W2952165733 created "2019-06-27" @default.
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- W2952165733 date "2006-07-07" @default.
- W2952165733 modified "2023-09-27" @default.
- W2952165733 title "Sharp threshold for hamiltonicity of random geometric graphs" @default.
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