Farber's conjecture for planar graphs

Knudsen, Ben

doi:10.1007/s00029-021-00702-w

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Farber's conjecture for planar graphs

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Knudsen, Ben
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00029-021-00702-w
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Citation

Knudsen, B. (2021). Farber's conjecture for planar graphs. Selecta Mathematica. New Series, 27(5): 90. doi:10.1007/s00029-021-00702-w.

Cite as: https://hdl.handle.net/21.11116/0000-0009-7944-3

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.