The University College London (UCL) Combinatorics Seminar takes place weekly on Tuesday, from 4pm to 5pm, in Taviton Street 16 Room 535. It is organised by Shoham Letzter.
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5 December 2022 - Viresh Patel (Queen Mary)
Hamilton cycles in regular oriented and directed graphs
Classical theorems of Dirac and of Ghouila-Houri establish the minimum degree theshold that guarantees the existence of a Hamilton cycle in a graph and in a directed graph respectively. (For oriented graphs, the degree threshold was established much more recently.) By imposing suitable regularity and/or connectivity conditions on graphs, one can lower the degree threshold at which a Hamilton cycle is guaranteed to appear, and this is quite well understood in the case of graphs. Conjectures of Kuhn and Osthus and of Jackson describe the corresponding situation for directed graphs and oriented graphs respectively. I will discuss approximate solutions to these conjectures. This is based on joint work with Allan Lo and Mehmet Akif Yildiz.
This talk will be in Gordon Square (26) Room B32.