Hamiltonicity-to-pancyclicity sprinkling principle
= Hamiltonicity-to-pancyclicity sprinkling principle
For a decreasing probability sequence $p(n)$, if $G(n,p(n))$ contains a <Hamilton cycle> <with high probability>, then $G(n,\min\{Cp(n),1\})$ is <pancyclic graph>[pancyclic] with high probability for every fixed sufficiently large $C$; three independent rounds suffice. One first exposes a Hamiltonian round and uses the independent sprinkled edges to create cycles of every shorter length.