The Hamiltonicity of essentially 9‐connected line graphs
Tomáš Kaiser, Petr Vrána · Journal of Graph Theory · 2020
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 line 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.