A graph G is N 2 -locally connected if for every vertex v in G, the edges not incident with v but having at least one end adjacent to v in G induce a connected graph. In 1990, Ryja Β΄c Λek conjectured that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. This conjecture is pro
Panconnectivity of locally connected claw-free graphs
β Scribed by Yu Sheng; Feng Tian; Bing Wei
- Book ID
- 108316336
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 91 KB
- Volume
- 203
- Category
- Article
- ISSN
- 0012-365X
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## Abstract A graph __G__ is locally __n__βconnected, __n__ β₯ 1, if the subgraph induced by the neighborhood of each vertex is __n__βconnected. We prove that every connected, locally 2βconnected graph containing no induced subgraph isomorphic to __K__~1,3~ is panconnected.
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.