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October 22, 2025Journal of the European Mathematical SocietyOpen Access

Geometric constructions for Ramsey–Turán theory

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Authors

HLHong LiuCRChristian ReiherMSMaryam Sharifzadeh

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Overview

Analysis reveals distinct asymptotic structures in Ramsey-Turán theory, suggesting new graph constructions for density issues.

Key Points

  • Asymptotic extremal structures differ significantly from the case when p=2, revealing new insights.
  • The construction of Bollobás–Erdős-type graphs using rational densities was successfully achieved with complex spheres.
  • Matching upper bounds were established, contributing valuable results to the field of extremal combinatorics.
  • Two major open problems were addressed, enhancing understanding of Ramsey-Turán theory's behavior.

Cite This Study

Liu et al. (2025) studied this question.

synapsesocial.com/papers/68f83321d24b29c969481ef7https://doi.org/10.4171/jems/1712
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