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In this paper, we propose a novel method to deal with a large number of faults existing in the system based on the PMC model. We derive a fault bound $T$ for a $N$-node ring based on cycle partition and Pigeonhole principle. Under this fault bound, it is guaranteed that at least one sequence obtained from cycle partition can be picked out and all nodes in this sequence can be identified. The corresponding ring diagnosis algorithm is then provided. Using this ring diagnosis method, we propose a five-round adaptive diagnosis scheme for networks containing Hamiltonian cycle. Simulations show that for Hamiltonian networks with node degree more than $3$, it can achieve almost complete diagnosis. [ABSTRACT FROM AUTHOR]