A local-global principle for vertex-isoperimetric problems
type: Item
instance of: scholarly article
title: A local-global principle for vertex-isoperimetric problems
zbMATH Open document ID: 1016.05043
DOI: 10.1016/S0012-365X(02)00431-4
author: Sergej L. Bezrukov
author: Oriol Serra
published in: Discrete Mathematics
publication date: 2002-12-02T00:00:00Z
review text: A total order \(\preceq\) on the vertex set of a graph \(G\) is called isoperimetric if the boundary (vertices at a distance \(1\)) of the sets of a fixed size is a minimum for the initial segment of that size in the order \(\preceq\), and if the ball (vertices at a distance at most \(1\)) is also an initial segment of the order \(\preceq\). Isoperimetric orders for the Cartesian powers \(G^n\) of a graph \(G\) under the simplicial order (vertices ordered by norm first and then lexicographically) \(\preceq^n\) for Cartesian products are studied. It is shown that the simplicial order \(\preceq^n\) is isoperimetric for each \(n \geq 1\) if and only if it is isoperimetric for \(n = 1, 2\).
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1838994
zbMATH Keywords: isoperimetric
zbMATH Keywords: Cartesian product
zbMATH Keywords: simplicial order
reviewed by: Ralph Faudree
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1838994