# A short note on graphs with long Thomason chains

@article{Brianski2022ASN,
title={A short note on graphs with long Thomason chains},
journal={Discret. Math.},
year={2022},
volume={345},
pages={112624}
}
• Published 6 March 2019
• Mathematics
• Discret. Math.
1 Citations

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## References

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The Complexity of Finding a Second Hmiltonian Cycle in Cubic Graphs
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.
THE COMPLEXITY OF THOMASON’S ALGORITHM FOR FINDING A SECOND HAMILTONIAN CYCLE
• Liang Zhong
• Mathematics
Bulletin of the Australian Mathematical Society
• 2018
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),
The Traveling Salesman Problem for Cubic Graphs
• D. Eppstein
• Computer Science, Mathematics
J. Graph Algorithms Appl.
• 2007
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
• Mathematics
• 2009
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.