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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| 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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| _version_ | 1832562775742742528 |
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| author | Brian Hopkins |
| author_facet | Brian Hopkins |
| author_sort | Brian Hopkins |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e1b4e202d2e04e5cacbadad9b9c00fe7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e1b4e202d2e04e5cacbadad9b9c00fe72025-02-03T01:21:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004301613161610.1155/S0161171204307118Hamiltonian paths on Platonic graphsBrian Hopkins0Department of Mathematics, Saint Peter's College, Jersey City 07306, NJ, USAWe 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.http://dx.doi.org/10.1155/S0161171204307118 |
| spellingShingle | Brian Hopkins Hamiltonian paths on Platonic graphs International Journal of Mathematics and Mathematical Sciences |
| title | Hamiltonian paths on Platonic graphs |
| title_full | Hamiltonian paths on Platonic graphs |
| title_fullStr | Hamiltonian paths on Platonic graphs |
| title_full_unstemmed | Hamiltonian paths on Platonic graphs |
| title_short | Hamiltonian paths on Platonic graphs |
| title_sort | hamiltonian paths on platonic graphs |
| url | http://dx.doi.org/10.1155/S0161171204307118 |
| work_keys_str_mv | AT brianhopkins hamiltonianpathsonplatonicgraphs |