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A universal exponent for homeomorphs

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Abstract

We prove a uniform bound on the topological Turán number of an arbitrary two-dimensional simplicial complex S: any two-dimensional complex on n vertices with at least CSn3−1/5 facets contains a homeomorph of S, where CS > 0 is a constant depending on S alone. This result, a two-dimensional analogue of a classical one-dimensonal result of Mader, sheds some light on an old problem of Linial from 2006.

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Acknowledgements

The first and second authors were partially supported by ERC Consolidator Grant 647678, and the third author wishes to acknowledge support from NSF grant DMS-1800521.

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Correspondence to Bhargav Narayanan.

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Keevash, P., Long, J., Narayanan, B. et al. A universal exponent for homeomorphs. Isr. J. Math. 243, 141–154 (2021). https://doi.org/10.1007/s11856-021-2156-7

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  • DOI: https://doi.org/10.1007/s11856-021-2156-7

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