Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, May 16, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Michael Hoffmann

Lower bounds for obstacle numbers

An obstacle representation of a graph G consists of a set of pairwise disjoint simply-connected closed regions in the plane and a one-to-one mapping of the vertices of G to points such that two vertices are adjacent in G if and only if the line segment that connects the two corresponding points does not intersect any obstacle. The obstacle number of a graph G is the smallest number of obstacles in an obstacle representation of G such that all obstacles are simple polygons; for the convex obstacle number, all obstacles must be convex polygons. In this talk, I will discuss lower bounds for obstacle numbers. Specifically, there is a constant c s.t. for every n there exists a graph on n vertices that has convex obstacle number at least cn. Joint work with Martin Balko, Steven Chaplick, Robert Ganian, Siddharth Gupta, Pavel Valtr, and Alexander Wolff.

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