Farber's conjecture for planar graphs

Abstract

We prove that the ordered configuration spaces of planar graphs have the highest possible topological complexity generically, as predicted by a conjecture of Farber. Our argument establishes the same generic maximality for all higher topological complexities. We include some discussion of the non-planar case, demonstrating that the standard approach to the conjecture fails at a fundamental level.

11 pages, 1 figure. Accepted for publication in Selecta Mathematica. May differ slightly from published from version