Powers of Hamiltonian cycles in randomly augmented Dirac graphs—The complete collection

Abstract

AbstractWe study the powers of Hamiltonian cycles in randomly augmented Dirac graphs, that is, ‐vertex graphs with minimum degree at least to which some random edges are added. For any Dirac graph and every integer , we accurately estimate the threshold probability for the event that the random augmentation contains the ‐th power of a Hamiltonian cycle.