Article ID Journal Published Year Pages File Type
4653613 European Journal of Combinatorics 2014 9 Pages PDF
Abstract

A class of graphs is nowhere dense if for every integer rr there is a finite upper bound on the size of complete graphs that occur as rr-minors. We observe that this recent 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. Expressed in terms of PAC learning, the concept classes definable in first-order logic in a subgraph-closed graph class have bounded sample complexity, if and only if the class is nowhere dense.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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