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arXiv · 2311.03868

The matroid of a graphing

László Lovász
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Abstract

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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László Lovász. 2023-11-07. The matroid of a graphing. https://arxiv.org/abs/2311.03868

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