A counterexample to the Bollob\'as-Riordan conjectures on sparse graph limits
Combinatorics
2021-11-08 v2
Abstract
Bollob\'as and Riordan, in their paper "Metrics for sparse graphs," proposed a number of provocative conjectures extending central results of quasirandom graphs and graph limits to sparse graphs. We refute these conjectures by exhibiting a sequence of graphs with convergent normalized subgraph densities (and pseudorandom -counts), but with no limit expressible as a kernel.
Keywords
Cite
@article{arxiv.2003.05272,
title = {A counterexample to the Bollob\'as-Riordan conjectures on sparse graph limits},
author = {Ashwin Sah and Mehtaab Sawhney and Jonathan Tidor and Yufei Zhao},
journal= {arXiv preprint arXiv:2003.05272},
year = {2021}
}