?ュ??瀛﹁??锛?Tomas Kaiser ????

?ュ??????浣?锛?University of West Bohemia

?ュ???堕?达?2024骞?0??23?ワ??ㄤ?锛?涓???14:30--15:30

?ュ???扮?癸? Zoom number  7226806999

?ュ????瑕?锛?Title: Had Dirac met with Kuratowski

  We will review the main problems and results on the existence of Hamilton cycles in sufficiently connected line graphs L(H), where H is a graph or a hypergraph. The point of departure is the well known conjecture of Thomassen that 4-connected line graphs (of graphs) are Hamiltonian. We will recall the ideas behind the proof of P. Vrana and the speaker of a weakening of this conjecture (for 5-connected line graphs with minimum degree at least 6), 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 of hypergraphs 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 hypergraph is 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.