Dense minor with bounded order and high minimum degree

For each positive integer $k$, a nonempty graph satisfying $e(G)\ge 11k|G|$ has a graph minor $H$ satisfyingThe density hypothesis is a lower bound. Reversing its inequality would be false for an edgeless graph. This auxiliary lemma can be used to establish a $7t\sqrt{\log t}$ upper bound for the complete graph minor density threshold.