In [4] Papadimitriou proposed to study the complexity of search problems for total functions, in which the existence of a solution is guaranteed via simple combinatorial arguments, but no efficient algorithmic solutions are known. See also [3, 5, 1] for other related works. One of the problems considered in [4] is the following: given a cubic graph G, and a Hamiltonian cycle C in G, compute a Hamiltonian cycle in G different than C. Smith's theorem asserts that such another cycle always exists… CONTINUE READING