Hamiltonicity of graphs perturbed by a random geometric graph

Abstract

We study Hamiltonicity in graphs obtained as the union of a deterministic n-vertex graph H with linear degrees and a d-dimensional random geometric graph Gd(n,r), for any d≥1. We obtain an asymptotically optimal bound on the minimum r for which a.a.s. H Gd(n,r) is Hamiltonian. Our proof provides a linear time algorithm to find a Hamilton cycle in such graphs.

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