A short note on graphs with long Thomason chains

@article{Brianski2022ASN,
  title={A short note on graphs with long Thomason chains},
  author={Marcin Bria'nski and Adam Szady},
  journal={Discret. Math.},
  year={2022},
  volume={345},
  pages={112624}
}
The Complexity of Iterated Reversible Computation
TLDR
The definition of IB is robust against variations in the type of reduction used in its definition, and in whether it requires f to have a polynomial-time inverse or to be computible by a reversible logic circuit.

References

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TLDR
An exponential lower bound is proved on the number of steps of Thomason's algorithm, which is an algorithm that given one Hamiltonian cycle in such a graph, computes another one.
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By Smith’s theorem, if a cubic graph has a Hamiltonian cycle, then it has a second Hamiltonian cycle. Thomason [‘Hamilton cycles and uniquely edge-colourable graphs’, Ann. Discrete Math. 3 (1978),
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TLDR
The algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the same time bound, and count the number of Hamiltonian cycles in time \(\mathcal{O}(2^{3n/8}n^{\mathcal O}(1)}) \approx {\rm 1.29684}^n\).
Analytic Combinatorics
TLDR
This text can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study, and is certain to become the definitive reference on the topic.