New irrelevant-vertex theorem for (k,d)-Folio gives linkage function ℓ(k) bounded by 2^{poly(k)}.
[Wor81] Nicholas C
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In planar and bounded-genus graphs, absence of k pairwise d-far S-T paths implies a vertex set of size f(d,k) whose d-neighborhood intersects every S-T path.
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Optimal Bounds for the k-Disjoint Paths Problem
New irrelevant-vertex theorem for (k,d)-Folio gives linkage function ℓ(k) bounded by 2^{poly(k)}.
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A coarse Menger's Theorem for planar and bounded genus graphs
In planar and bounded-genus graphs, absence of k pairwise d-far S-T paths implies a vertex set of size f(d,k) whose d-neighborhood intersects every S-T path.