Geometry Seminar

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Graphs with Nontrivial Planar Almost Embeddings

Speaker: Radoslav Fulek, NYU

Location: Warren Weaver Hall 1314

Date: Tuesday, February 20, 2024, 6 p.m.

Synopsis:

An almost embedding of a graph G is a drawing of G where only adjacent edges may cross. A drawing of a graph is reduced if it contains no empty bigon; equivalently, the number of crossings in the drawing cannot be decreased by homotopies of the edges that do not pass over the vertices. We characterize the class of graphs that have a reduced almost embedding on the sphere with at least one crossing. As an application we improve and generalize a recent result of Garaev about K5 minus an edge answering a question of A. Skopenkov and Karasev.

Joint work with J. Kynčl.

Notes:

A mix of in person and remote presentations; both types are live-streamed on Zoom and recorded.
In-person and remote talks are at different times.
See mailing list announcements for Zoom details or contact Boris Aronov.