A fundamental result of Mader from 1972 asserts that a graph of high average degree contains a highly connected subgraph with roughly the same average degree. We prove a lemma showing that one can strengthen Mader’s result by replacing the notion of high connectivity by the notion of vertex expansion. Another well known result in graph theory states that for every integer t there is a smallest real c(t), such that every n-vertex graph with c(t)n edges contains a Kt-minor. Fiorini, Joret, Theis… CONTINUE READING