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 Ξ΄ and the toughness t. It is shown that C is a Hamiltonian cycle or |C| β₯ (t + 1)Ξ΄ + t.
Tough Ramsey Graphs Without Short Cycles
β Scribed by Noga Alon
- Book ID
- 110420202
- Publisher
- Springer
- Year
- 1995
- Tongue
- English
- Weight
- 385 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0925-9899
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## Abstract Let __G__ be a toroidal graph without cycles of a fixed length __k__, and Ο~__l__~(__G__) the list chromatic number of __G__. We establish tight upper bounds of Ο~__l__~(__G__) for the following values of __k__: Β© 2009 Wiley Periodicals, Inc. J Graph Theory 65: 1β15, 2010.
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