International Journal of Mathematics and Mathematical Sciences (Jan 2004)

Hamiltonian paths on Platonic graphs

  • Brian Hopkins

DOI
https://doi.org/10.1155/S0161171204307118
Journal volume & issue
Vol. 2004, no. 30
pp. 1613 – 1616

Abstract

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We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topologically uniquely Hamiltonian.