A Cantor-Bernstein theorem for infinite matroids
Attila Jo\'o
TL;DR
This paper extends the Cantor-Bernstein theorem to infinite matroids, providing a unified matroidal framework that generalizes previous results on paths and spanning trees in infinite graphs.
Contribution
It introduces a novel matroidal generalization of the Cantor-Bernstein theorem applicable to infinite structures, unifying prior graph-specific theorems.
Findings
Established a common matroidal framework for infinite paths and spanning trees
Unified previous theorems into a single matroidal generalization
Extended Cantor-Bernstein concepts to infinite matroids
Abstract
We give a common matroidal generalisation of `A Cantor-Bernstein theorem for paths in graphs' by Diestel and Thomassen and `A Cantor-Bernstein-type theorem for spanning trees in infinite graphs' by ourselves.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Advanced Graph Theory Research · Markov Chains and Monte Carlo Methods