Seminars
Recent Results on Hamilton-Connected Line Graphs--11/21/23--Dr. Xiaofeng Gu--West Georgia University
Thomassen conjectured that every 4-connected line graph is Hamiltonian. The best result to date is due to Kaiser and Vrana, who proved that every 5-connected line graph of minimum degree at least 6 is Hamilton-connected. They also proved that every 3-connected essentially 9-connected line graph is Hamilton-connected, where a graph G is essentially k-connected if G has no vertex cut X of size less than k such that G-X has two nontrivial components. Some recent updates and related results will be presented in this talk.