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2002

A local-global principle for vertex-isoperimetric problems

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A local-global principle for vertex-isoperimetric problems
We consider the vertex-isoperimetric problem for cartesian powers of a graph G. A total order on the vertex set of G is called isoperimetric if the boundary of sets of a given size k is minimum for any initial segment of , and the ball around any initial segment is again an initial segment of . We prove a local-global principle with respect to the so-called simplicial order on Gn (see Section 2 for the definition). Namely, we show that the simplicial order n is isoperimetric for each n 1 iff it is so for n = 1, 2. Some structural properties of graphs that admit simplicial isoperimetric orderings are presented. We also discuss new relations between the vertex-isoperimetric problems and Macaulay posets.
Sergei L. Bezrukov, Oriol Serra
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2002
Where DM
Authors Sergei L. Bezrukov, Oriol Serra
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