## Abstract Our main result is the following theorem. Let __k__ ≥ 2 be an integer, __G__ be a graph of sufficiently large order __n__, and __δ__(__G__) ≥ __n__/__k__. Then: __G__ contains a cycle of length __t__ for every even integer __t__ ∈ [4, __δ__(__G__) + 1]. If __G__ is nonbipartite then
The number of cycle lengths in graphs of given minimum degree and girth
✍ Scribed by P. Erdős; R.J. Faudree; C.C. Rousseau; R.H. Schelp
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 333 KB
- Volume
- 200
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
This paper determines lower bounds on the number of different cycle lengths in a graph of given minimum degree k and girth g. The most general result gives a lower bound of ck ~.
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