Unavoidable Minors of Large 3-Connected Binary Matroids

We show that, for every integerngreater than two, there is a numberNsuch that every 3-connected binary matroid with at leastNelements has a minor that is isomorphic to the cycle matroid ofK3, n, its dual, the cycle matroid of the wheel withnspokes, or the vector matroid of the binary matrix (In|Jn−In), whereJnis then×nmatrix of all ones.