  Link failures in supply networks can have catastrophic consequences that can
lead to a complete collapse of the network. Strategies to prevent failure
spreading are thus heavily sought after. Here, we make use of a spanning tree
formulation of link failures in linear flow networks to analyse topological
structures that prevent failures spreading. In particular, we exploit a result
obtained for resistor networks based on the \textit{Matrix tree theorem} to
analyse failure spreading after link failures in power grids. Using a spanning
tree formulation of link failures, we analyse three strategies based on the
network topology that allow to reduce the impact of single link failures. All
our strategies do not reduce the grid's ability to transport flow or do in fact
improve it - in contrast to traditional containment strategies based on
lowering network connectivity. Our results also explain why certain
connectivity features completely suppress any failure spreading as reported in
recent publications.
