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Uniquely hamiltonian graphs for many sets of degrees
We give constructive proofs for the existence of uniquely hamiltonian graphs
for various sets of degrees. We give constructions for all sets with minimum 2
(a
trivial case), all sets with minimum 3 that contain an even number (for sets
without an even number it is known that no uniquely hamiltonian graphs exist),
and
all sets with at least two elements and minimum 4 where all other elements
are at least 10. For minimum degree 3 and 4, the constructions also give
3-connected graphs
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