Powers of Hamiltonian cycles in randomly augmented Dirac graphs -- the complete collection
Abstract
We study the powers of Hamiltonian cycles in randomly augmented Dirac graphs, that is, n-vertex graphs G with minimum degree at least (1/2+)n to which some random edges are added. For any Dirac graph and every integer m2, we accurately estimate the threshold probability p=p(n) for the event that the random augmentation G G(n,p) contains the m-th power of a Hamiltonian cycle.
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