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February 25, 2026Journal of Graph Theory

Positive Codegree Andrásfai–Erdős–Sós Theorem for the Generalized Triangle

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Authors

XLXizhi LiuSRSijie RenYWYì Wáng

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Overview

Positive codegree extension shows bipartiteness in uniform hypergraphs, implying new bounds on Turán numbers.

Key Points

  • This research aims to extend the Andrásfai–Erdős–Sós theorem to generalized triangles in hypergraphs, demonstrating conditions for bipartiteness.
  • Establish conditions for bipartiteness based on codegree in generalized triangle-free uniform hypergraphs.
  • Analyze the structure of edges and vertices based on given parameters.
  • Answer a question posed by previous researchers regarding hypergraph properties.
  • Every generalized triangle-free uniform hypergraph satisfying the codegree condition is shown to be partite.
  • This extension implies a new positive codegree Turán number for all uniform hypergraphs.
  • The findings provide a strong form answer to a question posed by Hou et al.

Cite This Study

Liu et al. (2026) studied this question.

synapsesocial.com/papers/699e921bf5123be5ed050192https://doi.org/10.1002/jgt.70012
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