The exact inner vertex-isoperimetric profile I_d(k) on the d-regular tree is determined, with sets optimal precisely when their boundary branching excess satisfies τ(D) ≤ d-2, and all minimizers admit a canonical decomposition into iterated gluings of full domains.
Title resolution pending
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
The Isoperimetric Problem in Regular Trees
The exact inner vertex-isoperimetric profile I_d(k) on the d-regular tree is determined, with sets optimal precisely when their boundary branching excess satisfies τ(D) ≤ d-2, and all minimizers admit a canonical decomposition into iterated gluings of full domains.