> Peterson graphs The plural here is confusing. Are you talking about the Petersen graph, on ten vertices? There does exist a constructivist proof of its non-H

> Peterson graphs The plural here is confusing. Are you talking about the Petersen graph, on ten vertices? There does exist a constructivist proof of its non-Hamiltonicity: merely enumerate every cycle of length ten and show that none are Hamiltonian. There is a class of objects called generalised Petersen graphs but these are usually Hamiltonian: https://core.ac.uk/download/pdf/82084439.pdf https://core.ac.uk/download/pdf/82084439.pdf