Grinberg's criterion applied to some non-planar graphs
Robertson ([3]) and independently, Bondy ([1]) proved that the generalized Petersen graph P(n,2) is non-hamiltonian if n == 5 (mod 6), while Thomason ([5]) proved that it has precisely 3 hamiltonian cycles if n == 3 (mod 6). The hamiltonian cycles in the remaining generalized Petersen graphs were en...
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my.um.eprints.111482014-12-18T00:39:15Z http://eprints.um.edu.my/11148/ Grinberg's criterion applied to some non-planar graphs Chia, G.L. Thomassen, C. QA Mathematics Robertson ([3]) and independently, Bondy ([1]) proved that the generalized Petersen graph P(n,2) is non-hamiltonian if n == 5 (mod 6), while Thomason ([5]) proved that it has precisely 3 hamiltonian cycles if n == 3 (mod 6). The hamiltonian cycles in the remaining generalized Petersen graphs were enumerated by Schwenk ([4]). In this note we give a short unified proof of these results using Grinberg's theorem. 2010-11 Conference or Workshop Item PeerReviewed application/pdf en http://eprints.um.edu.my/11148/1/Grinberg%27s_Criterion_Applied.pdf Chia, G.L. and Thomassen, C. (2010) Grinberg's criterion applied to some non-planar graphs. In: The China-Japan Joint Conference on Computation Geometry, Graphs and Applications, 03-06 Nov 2010, Dalian, China. |
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QA Mathematics Chia, G.L. Thomassen, C. Grinberg's criterion applied to some non-planar graphs |
| description |
Robertson ([3]) and independently, Bondy ([1]) proved that the generalized Petersen graph P(n,2) is non-hamiltonian if n == 5 (mod 6), while Thomason ([5]) proved that it has precisely 3 hamiltonian cycles if n == 3 (mod 6). The hamiltonian cycles in the remaining generalized Petersen graphs were enumerated by Schwenk ([4]). In this note we give a short unified proof of these results using Grinberg's theorem. |
| format |
Conference or Workshop Item |
| author |
Chia, G.L. Thomassen, C. |
| author_facet |
Chia, G.L. Thomassen, C. |
| author_sort |
Chia, G.L. |
| title |
Grinberg's criterion applied to some non-planar
graphs |
| title_short |
Grinberg's criterion applied to some non-planar
graphs |
| title_full |
Grinberg's criterion applied to some non-planar
graphs |
| title_fullStr |
Grinberg's criterion applied to some non-planar
graphs |
| title_full_unstemmed |
Grinberg's criterion applied to some non-planar
graphs |
| title_sort |
grinberg's criterion applied to some non-planar
graphs |
| publishDate |
2010 |
| url |
http://eprints.um.edu.my/11148/1/Grinberg%27s_Criterion_Applied.pdf http://eprints.um.edu.my/11148/ |
| _version_ |
1643688977815830528 |
| score |
13.251813 |