Median decompositions arise from any system of vertex cuts via Sageev's dual median graph, are uniquely minimal, satisfy median-width equals clique number on all graphs, and characterize proper geometric actions of groups on median graphs through canonical decompositions of Cayley graphs.
Hickingbotham
4 Pith papers cite this work. Polarity classification is still indexing.
4
Pith papers citing it
citation-role summary
background 2
citation-polarity summary
fields
math.CO 4years
2026 4verdicts
UNVERDICTED 4roles
background 2polarities
background 2representative citing papers
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.
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.
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.
citing papers explorer
-
Vertex cuts and median decompositions
Median decompositions arise from any system of vertex cuts via Sageev's dual median graph, are uniquely minimal, satisfy median-width equals clique number on all graphs, and characterize proper geometric actions of groups on median graphs through canonical decompositions of Cayley graphs.
-
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.
-
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.