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November 17, 2025MathematikaOpen Access

Many pentagons in triple systems

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Authors

DMDhruv MubayiJSJózsef SolymosiDMDhruv Mubayi

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Overview

Analysis reveals a new bound on pentagon copies in vertex graphs, suggesting geometric implications for triangular configurations.

Key Points

  • at least copies of a pentagon exist in an edge graph that is not triangle-free, indicating a strong relationship with triangle counts.
  • the new bound improves upon previous results, showing advancements in understanding graph properties among mathematicians.
  • observational analysis explores configurations yielding triangle-sharing points in geometric settings with implications for larger sets.
  • the findings underscore significant developments in geometric theorems and limits of exponent reductions in structured graphs.

Cite This Study

Mubayi et al. (2025) studied this question.

synapsesocial.com/papers/692509f6c0ce034ddc352c41https://doi.org/10.1112/mtk.70059
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Also Consider

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  3. 3On Optimal Point Sets Determining Distinct Triangles2024
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  5. 5A spectral Erd\H{o}s-Faudree-Rousseau theorem2024 · 1 citations