Two Sufficient Conditions for Hamilton and Dominating Cycles
We prove that if is a 2-connect graph of size (the number of edges) and minimum degree with , where when and when , then each longest cycle in is a dominating cycle. The exact analog of this theorem for Hamilton cycles follows easily from two known results according to Dirac and Nash-Williams...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/185346 |
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| _version_ | 1832549148638838784 |
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| author | Zh. G. Nikoghosyan |
| author_facet | Zh. G. Nikoghosyan |
| author_sort | Zh. G. Nikoghosyan |
| collection | DOAJ |
| description | We prove that if is a 2-connect graph of size (the number of edges) and minimum degree with , where when and when , then each longest cycle in is a dominating cycle. The exact analog of this theorem for Hamilton cycles follows easily from two known results according to Dirac and Nash-Williams: each graph with is hamiltonian. Both results are sharp in all respects. |
| format | Article |
| id | doaj-art-1fc7d2a1e3c14fef86ed729dfa8e65f6 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1fc7d2a1e3c14fef86ed729dfa8e65f62025-02-03T06:12:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/185346185346Two Sufficient Conditions for Hamilton and Dominating CyclesZh. G. Nikoghosyan0Institute for Informatics and Automation Problems, National Academy of Sciences, Street P. Sevak 1, Yerevan 0014, ArmeniaWe prove that if is a 2-connect graph of size (the number of edges) and minimum degree with , where when and when , then each longest cycle in is a dominating cycle. The exact analog of this theorem for Hamilton cycles follows easily from two known results according to Dirac and Nash-Williams: each graph with is hamiltonian. Both results are sharp in all respects.http://dx.doi.org/10.1155/2012/185346 |
| spellingShingle | Zh. G. Nikoghosyan Two Sufficient Conditions for Hamilton and Dominating Cycles International Journal of Mathematics and Mathematical Sciences |
| title | Two Sufficient Conditions for Hamilton and Dominating Cycles |
| title_full | Two Sufficient Conditions for Hamilton and Dominating Cycles |
| title_fullStr | Two Sufficient Conditions for Hamilton and Dominating Cycles |
| title_full_unstemmed | Two Sufficient Conditions for Hamilton and Dominating Cycles |
| title_short | Two Sufficient Conditions for Hamilton and Dominating Cycles |
| title_sort | two sufficient conditions for hamilton and dominating cycles |
| url | http://dx.doi.org/10.1155/2012/185346 |
| work_keys_str_mv | AT zhgnikoghosyan twosufficientconditionsforhamiltonanddominatingcycles |