Graph curvature and local discrepancy

IF 0.9 3区 数学 Q2 MATHEMATICS Journal of Graph Theory Pub Date : 2024-09-24 DOI:10.1002/jgt.23176
Paul Horn, Adam Purcilly, Alex Stevens
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引用次数: 0

Abstract

In recent years, discrete notions of curvature have been defined and exploited to understand various geometric properties of graphs; especially regarding heat flow, and spectral properties. In this paper, we study various combinatorial properties implied by satisfying the Bakry–Émery curvature dimension inequality C D ( , K ) $CD(\infty ,K)$ . In particular we derive a local discrepancy inequality, similar in spirit to the expander mixing lemma from spectral graph theory, which certifies a type of “local pseudo-randomness” of the edge set of the graph, for graphs satisfying a curvature lower bound. In addition, several other consequences are derived regarding graph connectivity and cycle statistics of the graph.

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图曲率和局部差异
近年来,曲率的离散概念被定义并用于理解图的各种几何性质;特别是关于热流和光谱特性。本文研究了满足Bakry -Émery曲率维不等式C D(∞)所隐含的各种组合性质。K) $CD(\infty ,K)$。特别地,对于满足曲率下界的图,我们导出了一个类似于谱图理论中的扩展混合引理的局部差异不等式,证明了图边缘集的一类“局部伪随机性”。此外,还得到了图连通性和图的循环统计的几个结果。
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来源期刊
Journal of Graph Theory
Journal of Graph Theory 数学-数学
CiteScore
1.60
自引率
22.20%
发文量
130
审稿时长
6-12 weeks
期刊介绍: The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .
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