Extraconnectivity of graphs with large minimum degree and girth
✍ Scribed by C. Balbuena; A. Carmona; J. Fàbrega; M.A. Fiol
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 824 KB
- Volume
- 167-168
- Category
- Article
- ISSN
- 0012-365X
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## 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
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 ~.
Suppose G and H are graphs. We say G is H-colorable if there is a homomorphism (edge-preserving vertex mapping) from G to H. We say a graph G is uniquely H-colorable if there is an onto homomorphism c from G to H, and any other homomorphism from G to H is the composition o o c of c with an automorph