中文摘要：

不包含2K2的图是指不包含一对独立边作为导出子图的图．Kriesell证明了所有4连通的无爪图的线图是哈密顿连通的．本文证明了如果图G不包含2K2并且不同构与K2，P3和双星图，那么线图L（G）是哈密顿图，进一步应用由Ryjacek引入的闭包的概念，给出了直径不超过2的2连通无爪图是哈密顿图这个定理的新的证明方法．

英文摘要：

A graph is called 2K2-free if it does not contain an independent pair of edges as an induced subgraph. Kriesell proved that all 4-connected line graphs of claw-free graph are Hamiltonian-connected. Motivated from this, in this note, we show that if G is 2K2-free and is not isomorphic to K2, P3 or a double star, then the line graph L（G） is Hamiltonian. Moreover, by applying the closure concept of claw-free graphs introduced by Ryjacek , we provide another proof for a theorem, obtained by Gould and independently by Ainouche et al., which says that every 2-connected claw-free graph of diameter at most 2 is Hamiltonian.