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.

Long Cycles in 2-Connected Hypergraphs--10/19/23--Dr. Ruth Luo--The University of South Carolina

Dirac proved that every n-vertex, 2-connected graph with minimum degree x contains a cycle of length at least min{n, 2x}. In this talk we present an analog for a long Berge cycles in uniform hypergraphs. In particular, the minimum degree condition required differs dramatically if the size of the edges is small or large. This is joint work with Alexandr Kostochka and Grace McCourt.

Divisibility Rules--9/22/23--Dr. Jan Zijlstra, Middle Tennessee State University