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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A generalisation of the matroid lift construction


Author: Geoff Whittle
Journal: Trans. Amer. Math. Soc. 316 (1989), 141-159
MSC: Primary 05B35
DOI: https://doi.org/10.1090/S0002-9947-1989-0957084-1
MathSciNet review: 957084
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Abstract: This paper introduces a general matroid-theoretic construction which includes, as special cases, elementary lifts of matroids and bias matroids of biased graphs. To perform the construction on a matroid $ M$, it is necessary (but not sufficient) to have a submodular function inducing $ M$. Elementary lifts are obtained when the submodular function chosen is the rank function of $ M$.

We define what is meant by a $ k$-induced matroid. These matroids simultaneously generalise matroids of graphs, transversal matroids and Dilworth truncations. They are induced by a particularly natural class of submodular functions. The effect of the above construction on $ k$-induced matroids using these natural submodular functions is studied. Results on minors of $ k$-induced matroids and the matroids obtained from them using the construction are given.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0957084-1
Article copyright: © Copyright 1989 American Mathematical Society