A limit conjecture on the number of Hamiltonian cycles on thin triangular grid cylinder graphs | Zendy

Olga Bodroža-Pantić | Zendy; Rade Doroslovački | Zendy; Harris Kwong | Zendy; M. Pantić | Zendy

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

Author(s) -

Olga Bodroža-Pantić,

Rade Doroslovački,

Harris Kwong,

M. Pantić

Publication year - 2017

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.2021

Subject(s) - conjecture , cylinder , grid , recurrence relation , combinatorics , hamiltonian (control theory) , mathematics , enumeration , hamiltonian path , discrete mathematics , graph , geometry , mathematical optimization

We continue our research in the enumeration of Hamiltonian cycles (HCs) on thin cylinder grid graphs Cm × Pn+1 by studying a triangular variant of the problem. There are two types of HCs, distinguished by whether they wrap around the cylinder. Using two characterizations of these HCs, we prove that, for fixed m, the number of HCs of both types satisfy some linear recurrence relations. For small m, computational results reveal that the two numbers are asymptotically the same. We conjecture that this is true for all m ≥ 2.

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