Long cycles in certain graphs of large degree
Let G be a connected graph of order n and X={x∈V:d(x)≥n/2}. Suppose |X|≥3 and G satisfies the modified Fan's condition. We show that the vertices of the block B of G containing X form a cycle. This generalizes a result of Fan. We also give an efficient algorithm to obtain such a cycle. The co...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200003653 |
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| _version_ | 1850212536298766336 |
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| author | Pak-Ken Wong |
| author_facet | Pak-Ken Wong |
| author_sort | Pak-Ken Wong |
| collection | DOAJ |
| description | Let G be a connected graph of order n and
X={x∈V:d(x)≥n/2}. Suppose
|X|≥3 and G satisfies the
modified Fan's condition. We show that the vertices of the block
B of G containing X form a cycle. This generalizes a result
of Fan. We also give an efficient algorithm to obtain such a
cycle. The complexity of this algorithm is O(n2). In case G is 2-connected, the condition |X|≥3 can be removed and G is hamiltonian. |
| format | Article |
| id | doaj-art-8a8802d69f764cc0807c77d84a73d56d |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8a8802d69f764cc0807c77d84a73d56d2025-08-20T02:09:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01241069169710.1155/S0161171200003653Long cycles in certain graphs of large degreePak-Ken Wong0Department of Mathematics and Computer Science, Seton Hall University, South Orange 07079, NJ, USALet G be a connected graph of order n and X={x∈V:d(x)≥n/2}. Suppose |X|≥3 and G satisfies the modified Fan's condition. We show that the vertices of the block B of G containing X form a cycle. This generalizes a result of Fan. We also give an efficient algorithm to obtain such a cycle. The complexity of this algorithm is O(n2). In case G is 2-connected, the condition |X|≥3 can be removed and G is hamiltonian.http://dx.doi.org/10.1155/S0161171200003653Cyclehamiltonian graphbipartite graphblockadjacency listmodified Fan's condition. |
| spellingShingle | Pak-Ken Wong Long cycles in certain graphs of large degree International Journal of Mathematics and Mathematical Sciences Cycle hamiltonian graph bipartite graph block adjacency list modified Fan's condition. |
| title | Long cycles in certain graphs of large degree |
| title_full | Long cycles in certain graphs of large degree |
| title_fullStr | Long cycles in certain graphs of large degree |
| title_full_unstemmed | Long cycles in certain graphs of large degree |
| title_short | Long cycles in certain graphs of large degree |
| title_sort | long cycles in certain graphs of large degree |
| topic | Cycle hamiltonian graph bipartite graph block adjacency list modified Fan's condition. |
| url | http://dx.doi.org/10.1155/S0161171200003653 |
| work_keys_str_mv | AT pakkenwong longcyclesincertaingraphsoflargedegree |