A graph G is locally connected if the subgraph induced by the neighbourhood of each vertex is connected. We prove that a locally connected graph G of orderp 2 4, containing no induced subgraph isomorphic to K1,31 is Hamilton-connected if and only if G is 3connected.
Every connected, locally connected graph is upper embeddable
✍ Scribed by Ladislav Nebeský
- Publisher
- John Wiley and Sons
- Year
- 1981
- Tongue
- English
- Weight
- 154 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0364-9024
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✦ Synopsis
Abstract
In this Note it is proved that every connected, locally connected graph is upper embeddable. Moreover, a lower bound for the maximum genus of the square of a connected graph is given.
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