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Isoperimetric Inequalities on Hexagonal Grids

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arxiv 1201.0697 v1 pith:GXV6ZFOW submitted 2012-01-03 math.CO math.MG

Berit Gru{ss}ien This is my paper · ORCID
classification math.COmath.MG
keywords hexagonalnumberboundsgivengridgridsinfinitelower
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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.

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