Abstract
Let G be a 2-connected graph of order n with x,y ∈ V(G). For u,v ∈ V(G), let P i[u, v] denote the path with i vertices which connects u and v. In this paper, we prove that if n ≥ 5 and |N G(u)∪N G(v)| +d G(w) ≥ n+1 for every triple of independent vertices u,v,w of G, then there exists a P i[x,y] in G for 5 ≤ i ≤ n, or G belongs to one of three exceptional classes. This implies a positive answer to a conjecture by Wei and Zhu [Graphs Combin. 14 (1998), 263-274].
| Original language | English |
|---|---|
| Pages (from-to) | 3-10 |
| Number of pages | 8 |
| Journal | Australasian Journal of Combinatorics |
| Volume | 47 |
| Publication status | Published - 2010 Jun 10 |
| Externally published | Yes |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
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Matsubara, R., Tsugaki, M., & Yamashita, T. (2010). A neighborhood and degree condition for panconnectivity. Australasian Journal of Combinatorics, 47, 3-10.