Enumerating all Hamilton Cycles and Bounding the Number of Hamilton Cycles in 3-Regular Graphs
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We describe an algorithm which enumerates all Hamilton cycles of a given 3-regular $n$-vertex graph in time $O(1.276^{n})$, improving on Eppstein's previous bound. The resulting new upper bound of $O(1.276^{n})$ for the maximum number of Hamilton cycles in 3-regular $n$-vertex graphs gets close to the best known lower bound of $\Omega(1.259^{n})$. Our method differs from Eppstein's in that he considers in each step a new graph and modifies it, while we fix (at the very beginning) one Hamilton cycle $C$ and then proceed around $C$, successively producing partial Hamilton cycles.
2000 ◽
Vol 10
(01)
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pp. 73-78
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2011 ◽
Vol 20
(4)
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pp. 617-621
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1998 ◽
Vol 58
(1)
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pp. 1-13
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Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
2016 ◽
Vol 26
(12)
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pp. 1650204
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1953 ◽
Vol 49
(1)
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pp. 59-62
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