## Abstract The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. The existence of regular graphs with given degree and girth pair is proved and simple bounds for their smallest order are developed. Several infinite classes of such graphs are constructed and it is
Graphs and digraphs with given girth and connectivity
β Scribed by Jiping Liu; ; Huishan Zhou
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 230 KB
- Volume
- 132
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper, we show that for any given two positive integers g and k with g > 3, there exists a graph (digraph) G with girth g and connectivity k. Applying this result, we give a negative answer to the problem proposed by M. Junger, G. Reinelt and W.R Pulleyblank (1985).
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