This paper addresses a problem posed by Oxley (Matroid Theory, Cambridge University Press, Cambridge, 1992) for matroids.We shall show that ifG 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. © 2004 Elsevier Inc. All rights reserved. MSC: 05C38; 05C40; 05C70

CONTRACTIBLE n-MANIFOLDS AND THE DOUBLE n-SPACE PROPERTY

We show that a space with a finite asymptotic dimension is embeddable in a non-positively curved manifold. Then we prove that if a uniformly contractible manifold X is uniformly embeddable in Rn or non-positively curved n-dimensional simply connected manifold then X × Rn is integrally hyperspherical. If a uniformly contractible manifold X of bounded geometry is uniformly embeddable into a Hilbe...