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| โฅ (t + 1)ฮด + t.
โฆ LIBER โฆ
Determinants and Longest Cycles of Graphs
โ Scribed by Ejov, Vladimir; Filar, Jerzy A.; Murray, Walter; Nguyen, Giang T.
- Book ID
- 118196999
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2008
- Tongue
- English
- Weight
- 161 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0895-4801
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It is well-known that the largest cycles of a graph may have empty intersection. This is the case, for example, for any hypohamiltonian graph. In the literature, several important classes of graphs have been shown to contain examples with the above property. This paper investigates a (nontrivial) cl