id: 06108803
dt: j
an: 06108803
au: Zhao, Kewen; Lin, Yue; Zhang, Ping
ti: One sufficient condition for Hamiltonian graphs involving distances.
so: Russ. Math. 56, No. 4, 38-43 (2012).
py: 2012
pu: Pleiades Publishing (Allerton Press, Inc.), New York; Springer, New York
la: EN
cc: 
ut: Hamiltonian graph; Ore condition; neighborhood union condition; Chen
    condition; new sufficient condition
ci: 
li: doi:10.3103/S1066369X12040056
ab: Summary: In 1990 G. T. Chen proved that if $G$ is a 2-connected graph of
    order $n$ and $2|N(x) \cup N(y)| + d(x) + d(y) \geq 2n - 1$ for each
    pair of nonadjacent vertices $x, y \in V (G)$, then $G$ is Hamiltonian.
    In this paper we prove that if $G$ is a 2-connected graph of order $n$
    and $2|N(x) \cup N(y)| + d(x)+d(y) \ge 2n-1$ for each pair of
    nonadjacent vertices $x, y \in V (G)$ such that $d(x, y) = 2$, then $G$
    is Hamiltonian.
rv: