Infinite dimensional finitely forcible graphon
Abstract
Graphons are analytic objects associated with convergent sequences of dense graphs. Finitely forcible graphons, i.e., those determined by finitely many subgraph densities, are of particular interest because of their relation to various problems in extremal combinatorics and theoretical computer science. Lovasz and Szegedy conjectured that the topological space of typical vertices of a finitely forcible graphon always has finite dimension, which would have implications on the minimum number of parts in its weak epsregular partition. We disprove the conjecture by constructing a finitely forcible graphon with the space of typical vertices that has infinite dimension.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 arXiv:
 arXiv:1404.2743
 Bibcode:
 2014arXiv1404.2743G
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Discrete Mathematics
 EPrint:
 doi:10.1112/plms.12203