A counterexample to the Bollobás–Riordan conjectures on sparse graph limits. (27th September 2021) - Sah, Ashwin; Sawhney, Mehtaab; Tidor, Jonathan; Zhao, Yufei
Abstract: Bollobás 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 C 4 -counts), but with no limit expressible as a kernel.