A conjecture on the number of Hamiltonian cycles on thin grid cylinder graphs

Olga Bodroža-Pantić 1 Harris Kwong 2 Milan Pantić 3
1 Department of Mathematics and Informatics [Novi Sad]
2 Mathematical Sciences Department [Fredonia, NY]
3 Department of Physics [Novi Sad]
Abstract : We study the enumeration of Hamiltonian cycles on the thin grid cylinder graph $C_m \times P_{n+1}$. We distinguish two types of Hamiltonian cycles, and denote their numbers $h_m^A(n)$ and $h_m^B(n)$. For fixed $m$, both of them satisfy linear homogeneous recurrence relations with constant coefficients, and we derive their generating functions and other related results for $m\leq10$. The computational data we gathered suggests that $h^A_m(n)\sim h^B_m(n)$ when $m$ is even.
Keywords : contractible curves thin grid cylinder generating functions Hamiltonian cycles
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Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (in progress) (1), pp.219--240
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Olga Bodroža-Pantić, Harris Kwong, Milan Pantić. A conjecture on the number of Hamiltonian cycles on thin grid cylinder graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (in progress) (1), pp.219--240. 〈hal-01196857〉

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