Yang et al. proved that every 3-connected, essentially 11-connected line graph is Hamilton-connected. This was extended by Li and Yang to 3-connected, essentially 10-connected graphs. Strengthening their result further, we prove that 3-connected, essentially 9-connected line graphs are Hamilton-connected. We use a method based on quasigraphs in combination with the discharging technique. The result extends to claw-free graphs.

中文翻译：

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本质上 9 连通的线图的哈密顿性

杨等人。证明了每一个 3-连通的，本质上是 11-连通的线图都是 Hamilton-connected。这被 Li 和 Yang 扩展到 3-connected，本质上是 10-connected 图。进一步加强他们的结果，我们证明了 3 个连通的，本质上是 9 个连通的线图是 Hamilton 连通的。我们使用基于拟图的方法结合放电技术。结果扩展到无爪图。