论文标题
在光谱图问题上的稳定定理的新证明
New proofs of stability theorems on spectral graph problems
论文作者
论文摘要
Simonovits稳定性定理和Nikiforov光谱稳定性定理都是在极端图理论中求解Turán数字的精确值的强大工具。最近，füredi[J。组合。理论ser。 B 115（2015）]提供了Simonovits稳定定理的简洁明了的证明。在本说明中，我们提出了针对某些极端图问题的统一处理，包括Nikiforov的光谱稳定性定理的简短证明和MA和QIU最近证明的集团稳定性定理[欧洲J. Combin。 84（2020）]。此外，还包括一些与$ p $ spectral Radius和无价拉普拉斯半径相关的极端问题。
Both the Simonovits stability theorem and the Nikiforov spectral stability theorem are powerful tools for solving exact values of Turán numbers in extremal graph theory. Recently, Füredi [J. Combin. Theory Ser. B 115 (2015)] provided a concise and contemporary proof of the Simonovits stability theorem. In this note, we present a unified treatment for some extremal graph problems, including short proofs of Nikiforov's spectral stability theorem and the clique stability theorem proved recently by Ma and Qiu [European J. Combin. 84 (2020)]. Moreover, some spectral extremal problems related to the $p$-spectral radius and signless Laplacian radius are also included.
