English

The matroid of a graphing

Combinatorics 2023-11-08 v1

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.

Keywords

Cite

@article{arxiv.2311.03868,
  title  = {The matroid of a graphing},
  author = {László Lovász},
  journal= {arXiv preprint arXiv:2311.03868},
  year   = {2023}
}

Comments

21 pages

R2 v1 2026-06-28T13:13:51.293Z