A Generalisation of the Matroid Lift Construction
نویسنده
چکیده
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 A/ , 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 ^-induced matroids using these natural submodular functions is studied. Results on minors of /(-induced matroids and the matroids obtained from them using the construction are given.
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