On matroids on edge sets of graphs with connected subgraphs as circuits
J. M. S. Sim oes-Pereira · Proceedings of the American Mathematical Society · 1973
It is proved that if F \mathcal {F} is a finite family of connected, finite graphs, then a graph G G exists such that the subgraphs of G G isomorphic to a member of the family cannot be regarded as the circuits of a matroid on the edge set of G G .