The paper finds the threshold probability for random subgraphs of Dirac graphs to admit Hamilton cycle transversals and derives optimal counting and packing corollaries that generalize single-graph Hamilton cycle results.
Hamiltonian lines in graphs whose vertices have sufficiently large valen- cies
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Robust Hamiltonicity in families of Dirac graphs
The paper finds the threshold probability for random subgraphs of Dirac graphs to admit Hamilton cycle transversals and derives optimal counting and packing corollaries that generalize single-graph Hamilton cycle results.