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.
Title resolution pending
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
citation-role summary
background 2
citation-polarity summary
fields
math.CO 3years
2026 3verdicts
UNVERDICTED 3roles
background 2polarities
background 2representative citing papers
Locally finite graphs with an excluded finite minor have the weak coarse Menger property with f depending only on k and g linear in r independent of k.
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.
citing papers explorer
-
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.
-
Coarse Menger property of quasi-minor excluded graphs and length spaces
Locally finite graphs with an excluded finite minor have the weak coarse Menger property with f depending only on k and g linear in r independent of k.
-
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.