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 ´c ˇek conjectured that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. This conjecture is pro
Hamiltonian circuits in N2-locally connected K1,3-free graphs
✍ Scribed by ZdeněK Ryjáček
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 407 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0364-9024
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✦ Synopsis
Abstract
There are many results concerned with the hamiltonicity of K~1,3~‐free graphs. In the paper we show that one of the sufficient conditions for the K~1,3~‐free graph to be Hamiltonian can be improved using the concept of second‐type vertex neighborhood. The paper is concluded with a conjecture.
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