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A counterexample to the Bollobás–Riordan conjectures on sparse graph limits
Published online by Cambridge University Press: 27 January 2021
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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- © The Author(s), 2021. Published by Cambridge University Press
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Supported by NSF Graduate Research Fellowship Program DGE-1122374.
Supported by NSF Award DMS-1764176, the MIT Solomon Buchsbaum Fund, and a Sloan Research Fellowship.