Graphs with cycle spaces generated by bounded-length cycles have the coarse Menger property, with corollaries for hyperbolic graphs, finitely presented groups, and planar graphs with bounded faces.
Asymptotic half-grid and full-grid minors
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
fields
math.CO 3years
2026 3verdicts
UNVERDICTED 3roles
background 1polarities
background 1representative citing papers
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.
citing papers explorer
-
A coarse Menger theorem for hyperbolic graphs, finitely presented groups, and more
Graphs with cycle spaces generated by bounded-length cycles have the coarse Menger property, with corollaries for hyperbolic graphs, finitely presented groups, and planar graphs with bounded faces.
-
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 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.