Nowhere dense graph classes, stability, and the independence property

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.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Hans Adler, Isolde Adler
• Keywords: Algorithmic Graph Theory, CORR 2010, Education, Finite Upper Bound, Tameness Notion