Pancyclism in claw-free graphs

A graph G is claw-free if G has no induced subgraph isomorphic to K
1,3
. And a graph G is pancyclic if for every m, 3 ≤ m ≤ | V(G)|, there is a cycle of length m. This paper considered neighbourhood union for any pair of nonadjacent vertices in claw-free graph and obtained the following theorem: If G is a 2-connected claw-free graph of order n 12 and
$\vert N(u) \cup N(v)\vert + \vert N(u) \cup N(w)\vert + \vert N(v)\cup N(w)\vert \geq 2n-1$
for any three pairwise nonadjacent vertices u, v, and w, then G is pancyclic.