FHCP challenge set: The first set of structurally difficult instances of the hamiltonian cycle problem

The FHCP Challenge Set, comprising of 1001 instances of Hamiltonian cycle prob-lem, is introduced. This set is the first to contain instancesof Hamiltonian cycleproblem for which the primary difficulty is the underlying graph structure, ratherthan simply size. A summary of the kinds of graphs contained in the FHCP Chal-lenge Set is given. A discussion of the results of the FHCP Challenge, a year-longcompetition to solve all instances of the FHCP Challenge Setfirst announced at the59th Annual Meeting for the Australian Mathematical Society, is also included.