Nowhere dense graph classes, stability, and the independence property
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- arXiv:
- arXiv:1011.4016
- Bibcode:
- 2010arXiv1011.4016A
- Keywords:
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- Mathematics - Logic;
- Computer Science - Discrete Mathematics;
- Computer Science - Logic in Computer Science;
- 05C75 (Primary) 03C13;
- 03C45 (Secondary);
- G.2.2;
- F.4.1
- E-Print:
- 9 pages