Aα-谱与Lovász θ数之间的联系

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-04-17 DOI:10.1016/j.laa.2025.04.007

Gabriel Coutinho , Thiago Oliveira

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引用次数: 0

摘要

我们展示了最小的α，使得α d +(1−α)A叼0至少是1/ (G)，在Nikiforov和Rojo（2017）的基础上显着改善了结果。事实上，我们展示了一个更强的联系：如果允许a的非零项变化，而D的非零项也相应变化，那么我们展示了这个最小的α实际上等于1/ (G)形式。我们还展示了作为该优化框架的应用而获得的其他结果，包括与Motzkin和Straus（1964）著名的ω(G)二次公式的联系。

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A connection between the Aα-spectrum and Lovász theta number

We show that the smallest α so that

α D + (1 - α) A ≽ 0

is at least

1 / ϑ (\overline{G})

, significantly improving upon a result due to Nikiforov and Rojo (2017). In fact, we display a stronger connection: if the nonzero entries of A are allowed to vary and those of D vary accordingly, then we show that this smallest α is in fact equal to

1 / ϑ (\overline{G})

. We also show other results obtained as an application of this optimization framework, including a connection to the well-known quadratic formulation for

ω (G)

due to Motzkin and Straus (1964).

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.