Nowhere dense graph classes, stability, and the independence property

Details Nowhere dense graph classes, stability, and the independence property Nowhere dense graph classes, stability, and the independence property

2010-11-17

arxiv.org/abs/1011.4016v1

Mathematics

Logic

9 pages

Scientific paper

A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of cliques that occur as (topological) r-minors. We observe that this tameness notion from algorithmic graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability and to not having the independence property.

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