Deletion and contraction in configuration spaces of graphs

Agarwal, Sanjana; Banks, Maya; Gadish, Nir; Miyata, Dane

doi:10.2140/agt.2021.21.3663

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Local Flexibility1

Graphs and Their Configuration Spaces1

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2021

2022

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Cited by 2 publications

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“…This simple but fundamental idea was first articulated in the pioneering work of [Świ01], as expanded and clarified in [CL18]. The version we give here, or one very close to it, was discovered by the authors of [ABGM21] in their search for a purely topological description of certain algebraic constructions of [ADCK19, ADCK20].…”

Section: Local Flexibilitymentioning

confidence: 69%

Farber’s conjecture for planar graphs

Knudsen

2021

Sel. Math. New Ser.

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We survey two decades of work on the (sequential) topological complexity of configuration spaces of graphs (ordered and unordered), aiming to give an account that is unifying, elementary, and self-contained. We discuss the traditional approach through cohomology, with its limitations, and the more modern approach through asphericity and the fundamental group, explaining how they are in fact variations on the same core ideas. We close with a list of open problems in the field.

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Section: Local Flexibilitymentioning

confidence: 69%