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Broersma, H.J. and Xiong, L. and Yoshimoto, K.
(2007)
Toughness and hamiltonicity in k-trees.
Discrete Mathematics, 307 (7-8).
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ISSN 0012-365X
*** ISI Impact 0,536 ***
Full text available as: Official URL: http://dx.doi.org/10.1016/j.disc.2005.11.051  AbstractWe consider toughness conditions that guarantee the existence of a hamiltonian cycle in  -trees, a subclass of the class of chordal graphs. By a result of Chen et al. 18-tough chordal graphs are hamiltonian, and by a result of Bauer et al. there exist nontraceable chordal graphs with toughness arbitrarily close to  . It is believed that the best possible value of the toughness guaranteeing hamiltonicity of chordal graphs is less than 18, but the proof of Chen et al. indicates that proving a better result could be very complicated. We show that every 1-tough 2-tree on at least three vertices is hamiltonian, a best possible result since 1-toughness is a necessary condition for hamiltonicity. We generalize the result to -trees for  : Let  be a -tree. If has toughness at least  , then is hamiltonian. Moreover, we present infinite classes of nonhamiltonian 1-tough -trees for each  .
| Item Type: | Article |
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| Research Group: | EWI-DMMP: Discrete Mathematics and Mathematical Programming |
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| Research Program: | CTIT-IE&ICT: Industrial Engineering and ICT |
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| ID Code: | 8088 |
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| Status: | Published |
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| Deposited On: | 13 July 2007 |
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| Refereed: | Yes |
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| International: | Yes |
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| ISI Impact Factor: | 0,536 |
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| More Information: | statisticsmetis |
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