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.
See also
Grinberg Graphs,
Nonhamiltonian Graph,
Tait's Hamiltonian Graph
Conjecture
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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 Graphs
Cite this as:
Weisstein, Eric W. "Faulkner-Younger Graphs."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Faulkner-YoungerGraphs.html
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