A counterexample to the Bollobás–Riordan conjectures on sparse graph limits
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Published:2021-01-27
Issue:5
Volume:30
Page:796-799
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ISSN:0963-5483
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Container-title:Combinatorics, Probability and Computing
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language:en
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Short-container-title:Combinator. Probab. Comp.
Author:
Sah Ashwin,Sawhney Mehtaab,Tidor Jonathan,Zhao Yufei
Abstract
AbstractBollobás 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science