The Faulkner-Younger graphs (Faulkner and Younger 1974) are the cubic polyhedral nonhamiltonian graphs on 42 and 44 vertices illustrated above that are counterexamples to Tait's Hamiltonian graph conjecture. Like the Grinberg graphs on 42 and 44 vertices, one can be constructed from the other simply by the contraction of a single edge.
Faulkner-Younger Graphs
See also
Grinberg Graphs, Nonhamiltonian Graph, Tait's Hamiltonian Graph ConjectureExplore with Wolfram|Alpha
References
Faulkner, G. B. and Younger, D. H. "Non-Hamiltonian Cubic Planar Maps." Discr. Math. 7, 67-74, 1974.Referenced on Wolfram|Alpha
Faulkner-Younger GraphsCite this as:
Weisstein, Eric W. "Faulkner-Younger Graphs." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Faulkner-YoungerGraphs.html