A counterexample to the Bollobás–Riordan conjectures on sparse graph limits
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 C4-counts), but with no limit expressible as a kernel.
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2019 ◽
Vol 138
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pp. 1-40
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