Matroidal families of finite connected nonhomeomorphic graphs exist
Thomas Andreae · Journal of Graph Theory · 1978
Abstract A matroidal family is a nonempty set ℱ of connected finite graphs such that for every arbitrary finite graph G the edge sets of the subgraphs of G which are isomorphic to an element of ℱ form a matroid on the edge set of G. In the present paper the question whether there are any matroidal families besides the four previously described by Simões‐Pereira is answered affirmatively. It is shown that for every natural number n ⩾ 2 there is a matroidal family that contains the complete graph with n vertices. For n = 4 this settles Simões‐Pereira's conjecture that there is a matroidal family containing all wheels.