图形的矩阵

IF 1.2 1区数学 Q1 MATHEMATICS

Journal of Combinatorial Theory Series B Pub Date : 2024-08-30 DOI:10.1016/j.jctb.2024.08.001

László Lovász

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引用次数: 0

摘要

图形是有界度图形的极限对象。我们将图形的 "循环矩阵 "定义为一个亚模态集合函数，其值在 [0,1] 范围内，它概括了有限图形的循环矩阵（直到归一化）。我们证明，对于本杰明-施拉姆收敛图序列，按节点数归一化的总秩收敛于极限图的总秩。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The matroid of a graphing

Graphings serve as limit objects for bounded-degree graphs. We define the “cycle matroid” of a graphing as a submodular setfunction, with values in $[0, 1]$ , which generalizes (up to normalization) the cycle matroid of finite graphs. We prove that for a Benjamini–Schramm convergent sequence of graphs, the total rank, normalized by the number of nodes, converges to the total rank of the limit graphing.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.