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Pancyclism in claw-free graphs

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2 Author(s)
Mei, Lu ; Department of Applied Mathematics, Tsinghua University, Beijing 100084 ; Zhengguang, Yu

A graph G is claw-free if G has no induced subgraph isomorphic to K1,3. 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.

Published in:

Tsinghua Science and Technology  (Volume:3 ,  Issue: 4 )