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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2015

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

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.
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Dates and versions

hal-01196857 , version 1 (10-09-2015)

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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, 2015, Vol. 17 no. 1 (1), pp.219--240. ⟨10.46298/dmtcs.2113⟩. ⟨hal-01196857⟩

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