The internally 4-connected binary matroids with no M(K5\e)-minor
  Let AG(3,2)xU(1,1) denote the binary matroid obtained from the direct sum of AG(3,2) and a coloop by completing the 3-point lines between every element in AG(3,2) and the coloop. We prove that every internally 4-connected binary matroid that does not have a minor isomorphic to M(K5\e) is isomorphic to a minor of (AG(3,2)xU(1,1))*. 
Dillon Mayhew and Gordon Royle
math.CO