Finding a small 3-connected minor maintaining a fixed minor and a fixed element
Let N and M be 3-connected matroids, where N is a minor of M on at least 4 elements, and let e be an element of M and not of N. Then, there exists a 3-connected minor of M that uses e, has N as a minor, and has at most 4 elements more than N. Results of Oxley, Seymour and Truemper follow from this theorem.
scientific article; zbMATH DE number 4041935