Topological cycle matroids of infinite graphs

TL;DR

This paper proves that the topological cycles in any infinite graph form a matroid, expanding the understanding of infinite graph structures and their properties.

Contribution

It introduces a new class of matroids derived from topological cycles in infinite graphs, which are neither finitary nor cofinitary.

Findings

Topological cycles induce a matroid in infinite graphs

The resulting matroid is generally neither finitary nor cofinitary

Provides a new framework for analyzing infinite graph structures

Abstract

We prove that the topological cycles of an arbitrary infinite graph induce a matroid. This matroid in general is neither finitary nor cofinitary.