Seymour's strengthening of Hadwiger's conjecture for graphs with no antitriangle

Let $G=(V,E)$ be a graph with no stable set of size $3$, and let a prevertex be a connected subgraph contracted to one vertex in a minor. Seymour's strengthening. The graph $G$ has a complete minor of size at least $|V|/2$ using only edges or single vertices as prevertices.

This strengthens Hadwiger's conjecture in the dense regime where the graph has no stable set of size $3$. The source presents it as conjectural and studies partial results and counterexamples to related generalizations.