This paper addresses a problem posed by Oxley (Matroid Theory, Cambridge University Press, Cambridge, 1992) for matroids. We shall show that if G is a 2-connected graph which is not a multiple edge, and which has no K5-minor, then G has two edge-disjoint non-trivial bonds B for which G/B is 2-connected.
['Sean McGuinness']
Contractible bonds in graphs