Barnette's conjecture

item It is known that this is not true if you remove the "bipartite" condition, but the smallest 3-connected cubic planar graph which is not Hamiltonian has 38 vertices. item Holton, Manvel, and McKay [HMM] proved (using computers) that all graphs having fewer than 66 vertices satisfy the conjecture. [HMM] Derek A.Holton, Bennet Manvel, Brendan D. McKay, Hamiltonian cycles in cubic 3-connected bipartite planar graphs, J. Combin. Theory Ser. B 38 (1985) 279-297. MathSciNet This is nice idea. This is to announce that the conjecture remains true up to 84 vertices, inclusive. The method used was the same as in the 1985 paper, but took advantage of two developments. Thank you. Select your preferred way to display the comments and click "Save settings" to activate your changes.