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Generalized Andr\'{a}sfai--Erd\H{o}s--S\'{o}s theorems for odd cycles

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arxiv 2409.11950 v1 pith:AUT66WRS submitted 2024-09-18 math.CO

Zian Chen , Jianfeng Hou , Caiyun Hu , Xizhi Liu This is my paper · ORCID
classification math.CO
keywords andrcitecyclesgeneralizedresultss--ssfai--erdtheorems
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In this note, we establish Andr\'{a}sfai--Erd\H{o}s--S\'{o}s-type stability theorems for two generalized Tur\'{a}n problems involving odd cycles, both of which are extensions of the Erd\H{o}s Pentagon Problem. Our results strengthen previous results by Lidick\'{y}--Murphy~\cite{LM21} and Beke--Janzer~\cite{BJ24}, while also simplifying parts of their proofs.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exact Tur\'{a}n number of the Fano plane in the $\ell_2$-norm

    math.CO 2025-07 conditional novelty 8.0 of 10

    For large n, the balanced complete bipartite 3-graph is the unique extremal construction for the ℓ2-norm Turán problem of the Fano plane, confirming a conjecture of Balogh-Clemen-Lidický.

  2. Interpolating chromatic and homomorphism thresholds

    math.CO 2025-02 conditional novelty 8.0 of 10

    The authors determine the exact VC-dimension-interpolated homomorphism thresholds for cliques and prove the blowup threshold of odd cycles C_{2k-1} is 1/(2k-1).

  3. Spectral generalized Tur\'{a}n problems

    math.CO 2025-07 conditional novelty 6.0 of 10

    The paper introduces spectral generalized Turán numbers, proves a general transfer theorem from counting stability to spectral extremality, and derives a spectral Erdős Pentagon Theorem and an entropy formula.

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