Lift Contractions

We introduce and study a new containment relation in graphs – lift contractions. H is a lift contraction of G if H can be obtained from G by a sequence of edge lifts and edge contractions. We show that a graph contains every n-vertex graph as a lift contraction, if (1) its treewidth is large enough, or (2) its pathwidth is large enough and it is 2-connected, or (3) its order is large enough and its minimum degree is at least 3.