Generalizations of the geometric de Bruijn Erdős Theorem

Abstract: A classic Theorem of de Bruijn and Erdős states that every noncollinear set of n points in the plane determines at least n distinct lines. The line L(u, v) determined by two points u, v in the plane consists of all points p such that

  • dist(p, u) + dist(u, v) = dist(p, v) (i.e. u is between p and v) or
    • dist(u, p) + dist(p, v) = dist(u, v) (i.e. p is between u and v) or
    • dist(u, v) + dist(v, p) = dist(u, p) (i.e. v is between u and p).

With this definition of line L(uv) in an arbitrary metric space (V, dist), Chen
and Chvátal conjectured that every metric space on n points, where n is at least 2, has at least n distinct lines or a line that consists of all n points. The
talk will survey results on and around this conjecture.

Date: May 08, 2019 at 14:30:00 h
Venue: Av República 701, Sala 33.
Speaker: Pierre Aboulker
Affiliation: U. Nice-Sophia-Antipolis
Coordinator: Prof. José Verschae
More info at:
Event website
Abstract:
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Posted on May 15, 2019 in AGCO, Seminars