✦ LIBER ✦
Graphs such that every two edges are contained in a shortest cycle
✍ Scribed by Nathalie Homobono; Claudine Peyrat
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 665 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
A graph G is said to have depth 6 if every path of length d + 1 is contained in a shortest cycle. First we answer by the negative a problem of Neumaier [2], by constructing for every 6, a graph of depth 6 which is neither a cyck nor a uniform subdivision of another graph. Then we characterize the graphs G such that every two edges are contained in a shortest cycle and we show that G is a uniform subdivision of a regular graph of girth 20, a semi-regular graph of girth 20 or a multigraph on two vertices.