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Longest cycles in polyhedral graphs

โœ Scribed by Hansjoachim Walther


Book ID
112886851
Publisher
The Hebrew University Magnes Press
Year
1993
Tongue
English
Weight
254 KB
Volume
83
Category
Article
ISSN
0021-2172

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In this article, we establish bounds for the length of a longest cycle C in a 2-connected graph G in terms of the minimum degree ฮด and the toughness t. It is shown that C is a Hamiltonian cycle or |C| โ‰ฅ (t + 1)ฮด + t.

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There is a constructed sequence of polyhedral cyclically 5-connected cubic non-hamiltonian graphs having only 5-gons and 8-gons as faces.