Verifies stronger coarse balanced separator conjecture for all r in K_{t,t}-induced-minor-free graphs of bounded clique number via a polynomial-size hitting set Z for large balls on any Y.
arXiv preprint arXiv:2502.20182 , year=
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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.
Graphs excluding any fixed H as a d-fat minor admit balanced separators coverable by O(n^{1/2+ε}) radius-r balls, with a poly-time algorithm to find the separator or the fat model.
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Coarse Balanced Separators in Biclique-Induced-Minor-Free Graphs
Verifies stronger coarse balanced separator conjecture for all r in K_{t,t}-induced-minor-free graphs of bounded clique number via a polynomial-size hitting set Z for large balls on any Y.
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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.
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Coarse Balanced Separators in Fat-Minor-Free Graphs
Graphs excluding any fixed H as a d-fat minor admit balanced separators coverable by O(n^{1/2+ε}) radius-r balls, with a poly-time algorithm to find the separator or the fat model.