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 C4-counts), but with no limit expressible as a kernel.

中文翻译：

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关于稀疏图极限的 Bollobás-Riordan 猜想的反例

Bollobás 和 Riordan 在他们的论文 'Metrics for sparse graphs' 中提出了一些具有挑战性的猜想，将拟随机图的中心结果和图限制扩展到稀疏图。我们通过展示一系列具有收敛归一化子图密度（和伪随机C4-counts)，但没有限制可表示为内核。