Isoperimetric Inequalities on Hexagonal Grids
Combinatorics
2012-01-04 v1 Metric Geometry
Abstract
We consider the edge- and vertex-isoperimetric probem on finite and infinite hexagonal grids: For a subset W of the hexagonal grid of given cardinality, we give a lower bound for the number of edges between W and its complement, and lower bounds for the number of vertices in the neighborhood of W and for the number of vertices in the boundary of W. For the infinite hexagonal grid the given bounds are tight.
Cite
@article{arxiv.1201.0697,
title = {Isoperimetric Inequalities on Hexagonal Grids},
author = {Berit Grußien},
journal= {arXiv preprint arXiv:1201.0697},
year = {2012}
}