Work

The matroid of a graphing

Year: 2024

Type: article

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.

Source: Journal of Combinatorial Theory Series B

DOI: 10.1016/j.jctb.2024.08.001

Author: László Lovász

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,560

Funders: European Resuscitation Council, European Research Council

Award: G5435431566