Nowhere dense graph classes, stability, and the independence property [article]

Hans Adler, Isolde Adler
2010 arXiv   pre-print
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.
arXiv:1011.4016v1 fatcat:ugcfw2bh4rfuxkeabtvjcmpfee