A graph G=(V,E) is called l-mixed p-connected if G-S-L is connected for all pairs S, L with S⊆V, L⊆E, amd l|S|+|L|<p. This notion is a common generalisation of m-vertex-connectivity (l=1,p=m) and m-edge-connectivity (l⩾m, p=m). We show how to use maximum adjacency orderings to find sparse certificates and removable cycles in l-mixed p-connected graphs in linear time.
