A counterexample to the Bollobás–Riordan conjectures on sparse graph limits
Name
2003.05272.pdf
Description
Submitted version
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119.03 KB
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Author(s)
Sah, Ashwin
Sawhney, Mehtaab
Tidor, Jonathan
Zhao, Yufei
Date Issued
2021
Journal
Combinatorics Probability and Computing
Publisher
Cambridge University Press (CUP)
Version
Original manuscript
Abstract
© The Author(s), 2021. Published by Cambridge University Press. 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1017/S0963548321000031
