2010/11/22 by Henning Bruhn, Bruhn, Henning, Reinhard Diestel +1 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Graph Labeling and Dimension Problems #math.CO
paper · pdf · doi:10.48550/arxiv.1011.4749
Figure corrected
openalex publication_date 2010/11/22 · arxiv created 2012/07/10 · arxiv updated 2012/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infinite matroids must have non-finitary duals. In this paper we illustrate the new theory by exhibiting its implications for the cycle and bond matroids of infinite graphs. We also describe their algebraic cycle matroids, those whose circuits are the finite cycles and double rays, and determine their duals. Finally, we give a sufficient condition for a matroid to be representable in a sense adapted to infinite matroids. Which graphic matroids are representable in this sense remains an open question.