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arXiv · 2001.00042

The hamiltonicity of essentially 9-connected line graphs

Tomáš Kaiser·Petr Vrána
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Abstract

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.

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Tomáš Kaiser, Petr Vrána. 2019-12-31. The hamiltonicity of essentially 9-connected line graphs. https://arxiv.org/abs/2001.00042

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