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This article forms an introduction to delta-matroids and multimatroids, aimed mainly at graph and matroid theorists. It is loosely based on a talk given at the MATRIX workshop on Uniqueness and Discernment in Graph Polynomials, 16–27th October 2023. Basic definitions, results and examples of delta-matroids and multimatroids are presented. We highlight the link between delta-matroids and both 2- and 3-matroids, and give a proof that the 3-matroid associated with an embedded graph is genuinely a tight multimatroid. The emphasis here is on providing the reader with the background needed to read papers and undertake research on deltamatroids and multimatroids, particularly those associated with embedded graphs.

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A Primer on Delta-matroids and Multimatroids

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  • 发表日期：

    2025年

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  • Steven Noble

摘要

This article forms an introduction to delta-matroids and multimatroids, aimed mainly at graph and matroid theorists. It is loosely based on a talk given at the MATRIX workshop on Uniqueness and Discernment in Graph Polynomials, 16–27th October 2023. Basic definitions, results and examples of delta-matroids and multimatroids are presented. We highlight the link between delta-matroids and both 2- and 3-matroids, and give a proof that the 3-matroid associated with an embedded graph is genuinely a tight multimatroid. The emphasis here is on providing the reader with the background needed to read papers and undertake research on deltamatroids and multimatroids, particularly those associated with embedded graphs.