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 |
Externally published | Yes |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
Cite this
A neighborhood and degree condition for panconnectivity. / Matsubara, Ryota; Tsugaki, Masao; Yamashita, Tomoki.
In: Australasian Journal of Combinatorics, Vol. 47, 2010, p. 3-10.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A neighborhood and degree condition for panconnectivity
AU - Matsubara, Ryota
AU - Tsugaki, Masao
AU - Yamashita, Tomoki
PY - 2010
Y1 - 2010
N2 - 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].
AB - 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].
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UR - http://www.scopus.com/inward/citedby.url?scp=77953158515&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:77953158515
VL - 47
SP - 3
EP - 10
JO - Australasian Journal of Combinatorics
JF - Australasian Journal of Combinatorics
SN - 1034-4942
ER -