Every k-edge-connected graph has a polynomially constructible spanning tree that is O(1/k)-thin for all η-near-minimum cuts with η = 1/40.
and Stein, Clifford , title =
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Strengthens the conditional running-time lower bound for Global Label Min-Cut under ETH to (np)^{o(log n / log log n)} via a deterministic reduction.
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Thin Trees for Near Minimum Cuts
Every k-edge-connected graph has a polynomially constructible spanning tree that is O(1/k)-thin for all η-near-minimum cuts with η = 1/40.
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A Stronger Conditional Running-Time Lower Bound for Global Label Min-Cut
Strengthens the conditional running-time lower bound for Global Label Min-Cut under ETH to (np)^{o(log n / log log n)} via a deterministic reduction.