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Thin spanning trees and their algorithmic applications

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SNAW01 - Graph limits and statistics

Motivated by Jaeger's modular orientation conjecture, Goddyn asked the following question: 

A spanning tree of a graph G is called epsilon-thin if it contains at most an epsilon fraction of the edges of each cut in that graph. Is there a function f:(0,1)→ ℤ such that every f(epsilon)-edge-connected graph has an epsilon-thin spanning tree?
I will talk about our journey in search of such thin trees, their applications concerning traveling salesman problems, and unexpected connections to graph sparsification and the Kadison-Singer problem.

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This talk is part of the Isaac Newton Institute Seminar Series series.

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