Asymptotic dimension of minor-closed families and beyond
Chun-Hung Liu
Abstract:The asymptotic dimension of metric spaces is an important notion in geometric group theory introduced by Gromov. The metric spaces considered in this paper are the ones whose underlying spaces are the vertex-sets of graphs and whose metrics are the distance functions in graphs. A standard compactness argument shows that it suffices to consider the asymptotic dimension of classes of finite graphs.In this paper we prove that the asymptotic dimension of any minor-closed family, any class of graphs of bounded tree… Show more
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