Dense minor with bounded order and high minimum degree
= Dense minor with bounded order and high minimum degree
For each positive integer $k$, a nonempty <graph> satisfying $e(G)\geq11k|G|$ has a <graph minor> $H$ satisfying
$$
|H|\leq11k+2,\qquad 2\delta(H)\geq |H|+4k-1.
$$
The 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>.