The smallest non-Hamiltonian 3-connected cubic planar graphs have 38 vertices
We show that all 3-connected cubic planar graphs on 36 or fewer vertices are hamiltonian, thus extending results of Lederberg, Butler, Goodey, Wegner, Okamura and Barnette. Furthermore, the only non-hamiltonian examples on 38 vertices which are not cyclically 4-connected are the six graphs which have been found by Lederberg, Barnette and Bosák.
scientific article; zbMATH DE number 3981218