Hamiltonian paths on Platonic graphs
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204307118 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |