@article {IOPORT.05879537,
    author       = {Matsubara, Ryota and Tsugaki, Masao and Yamashita, Tomoki},
    title        = {A neighborhood and degree condition for panconnectivity.},
    year         = {2010},
    journal      = {The Australasian Journal of Combinatorics},
    volume       = {47},
    issn         = {1034-4942},
    pages        = {3-10},
    publisher    = {Published for the Combinatorial Mathematics Society of Australasia by the Centre for Discrete Mathematics and Computing, the University of Queensland, Brisbane, QLD},
    abstract     = {Summary: Let $G$ be a 2-connected graph of order $n$ with $x,y\in V(G)$. For $u, v\in V(G)$, let $P_i[u, v]$ denote the path with $i$ vertices which connects $u$ and $v$. In this paper, we prove that if $n\ge 5$ and $|N_G(u)\cup N_G(v)|+ d_G(w)\ge n+ 1$ for every triple of independent vertices $u$, $v$, $w$ of $G$, then there exists a $P_i [x, y]$ in $G$ for $5\le i\le n$, or $G$ belongs to one of three exceptional classes. This implies a positive answer to a conjecture by {\it B. Wei} and {\it Y. Zhu} [``On the panconnectivity of graphs with large degrees and neighborhood unions,'' Graphs Comb. 14, No.\,3, 263--274 (1998; Zbl 0906.05039)].},
    identifier   = {05879537},
}