报告学者：Tomas Kaiser教授

报告者单位：University of West Bohemia

报告时间：2024年10月23日（周三）下午14:30--15:30

报告地点：Zoom number 7226806999

报告摘要：Title: Had Dirac met with Kuratowski

We will review the main problems and results on the existence of Hamiltoncycles in sufficiently connected line graphs L(H), where H is a graph or ahypergraph. The point of departure is the wellknown conjecture of Thomassen that 4-connected line graphs (of graphs) are Hamiltonian. We will recall theideas behind the proof of P. Vrana and the speaker of a weakening of this conjecture (for 5-connected line graphs with minimum degree at least6), phrasing them as in the recent simplified reformulation. We will show how similar ideas can be applied to handle graphs with sufficient essential connectivity. Do line graphs ofhypergraphs of bounded rank behave similarly to line graphs of graphs? Gu et al. conjectured that for every r ≥ 2, there exists an integer f(r) such that every f(r)-connected line graph of a rank r hypergraphis Hamiltonian. We will outline a proof of the r=3 case of this conjecture and discuss a possible approach to the problem for higher r.

The talk is based on joint work with Petr Vrana.