A Matroid Reconstruction Result
Allan D. Mills · Combinatorics Probability Computing · 1994
Suppose M and N are distinct matroids on a set E such that, for every e ∈ E, the deletion of e from M equals the deletion of e from N or the contraction of e from M equals the contraction of e from N. In this note we prove that, apart from some easily specified exceptions, one of M and N must be a relaxation of the other.