Generalized Andr\'{a}sfai--Erd\H{o}s--S\'{o}s theorems for odd cycles
Zian Chen, Jianfeng Hou, Caiyun Hu, and Xizhi Liu
TL;DR
This paper extends classical stability theorems to generalized Turán problems involving odd cycles, improving and simplifying previous results related to the Erdős Pentagon Problem.
Contribution
It establishes new stability theorems for generalized Turán problems with odd cycles, extending and simplifying prior work in the area.
Findings
Strengthens previous stability results for odd cycle Turán problems
Provides simplified proofs for generalized Erdős Pentagon-type theorems
Extends classical theorems to broader classes of graphs
Abstract
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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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Analytic Number Theory Research