László Lovász
Published 2023-11-07Version 1
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.
On graphs uniquely defined by their $k$-circular matroids
Isomorphism for even cycle matroids - I
Cycle Matroids of Graphings: From Convergence to Duality
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