Towards a splitter theorem for internally 4-connected binary matroids III

This paper proves a preliminary step towards a splitter theorem for internally 4-connected binary matroids. In particular, we show that, provided M or M⁎ is not a cubic Möbius or planar ladder or a certain coextension thereof, an internally 4-connected binary matroid M with an internally 4-connected proper minor N either has a proper internally 4-connected minor M′ with an N-minor such that |E(M)−E(M′)|⩽3 or has, up to duality, a triangle T and an element e of T such that M\e has an N-minor and has the property that one side of every 3-separation is a fan with at most four elements.