Finitely forcible graphons

Authors:
L. Lovász;B. Szegedy
Affiliations:
Eotvos Lorand University, Institute of Mathematics, 1518 Budapest, Pf. 120, Hungary;Department of Mathematics, University of Toronto, Toronto, Ontario, Canada
Venue:
Journal of Combinatorial Theory Series B
Year:
2011

Citing 5
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Abstract

We investigate families of graphs and graphons (graph limits) that are determined by a finite number of prescribed subgraph densities. Our main focus is the case when the family contains only one element, i.e., a unique structure is forced by finitely many subgraph densities. Generalizing results of Turan, Erdos-Simonovits and Chung-Graham-Wilson, we construct numerous finitely forcible graphons. Most of these fall into two categories: one type has an algebraic structure and the other type has an iterated (fractal-like) structure. We also give some necessary conditions for forcibility, which imply that finitely forcible graphons are ''rare'', and exhibit simple and explicit non-forcible graphons.