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

Date and Time: Tuesday, April 02, 2024, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Rajko Nenadov (University of Auckland, New Zealand)

Global rigidity of random graphs

Consider the Erdos-Renyi random graph process in which we start with an empty graph G(0) on the vertex set [n], and in each step form G(i) from G(i-1) by adding one new edge chosen uniformly at random. Resolving a conjecture by Benjamini and Tzalik, we show that w.h.p. as soon as G(m) has minimum degree 2 it is globally rigid in the following sense: For any function d:E(G(m))-> R, there exists at most one injective function f:[n]-> R(up to isometry) such that d(ij) = |f(i) - f(j)| for every edge ij in G(m). This is joint work with Richard Montgomery, Julien Portier, and Tibor Szabó.

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