Dear all,
There will be a noon seminar this Thursday, 5 June, given by Raphael Steiner. Please find the talk details below.
Please note the different time and room from usual!
Best regards, Misha Tyomkyn.
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On longest paths and cycles in graphs Raphael Steiner ETH Zurich June 5, 2025, 13:00 in S10
Abstract In this talk I will present some recent work, joint with various collaborators, on longest paths and cycles in graphs. First, I will discuss three conjectures due to Lovasz (1969), Thomassen (1978) and Smith (1984), respectively, regarding the length and intersections of longest paths and cycles in (vertex-transitive) graphs, and present improved bounds towards these conjectures. If time permits, I will also present some recent new results on the corresponding problem for directed graphs.
Motivated by and related to these conjectures I will then present an improved upper bound for another well-known problem, going back to an old question of Gallai from 1966, namely: How many vertices are needed to hit all longest paths (cycles) in a connected (2-connected) graph?
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