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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A decomposition-based framework finds entire sets of irrelevant vertices in linear time on bounded-genus graphs, enabling linear-time algorithms for minor containment, disjoint paths, and deletion problems.
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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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Finding irrelevant vertices in linear time on bounded-genus graphs
A decomposition-based framework finds entire sets of irrelevant vertices in linear time on bounded-genus graphs, enabling linear-time algorithms for minor containment, disjoint paths, and deletion problems.