Matroid and Tutte-connectivity in infinite graphs

TL;DR

This paper explores the relationship between matroid connectivity and Tutte-connectivity in infinite graphs, demonstrating that certain cycle matroids share the same connectivity function and that Tutte-connectivity remains invariant under dual graph operations.

Contribution

It establishes a connection between matroid and Tutte-connectivity in infinite graphs and shows the invariance of Tutte-connectivity under duality for such graphs.

Findings

Cycle matroids have identical connectivity functions.

Tutte-connectivity is invariant under graph duality.

Matroid connectivity relates to Tutte-connectivity in infinite graphs.

Abstract

We relate matroid connectivity to Tutte-connectivity in an infinite graph. Moreover, we show that the two cycle matroids, the finite-cycle matroid and the cycle matroid, in which also infinite cycles are taken into account, have the same connectivity function. As an application we re-prove that, also for infinite graphs, Tutte-connectivity is invariant under taking dual graphs.