Minimum degree k implies K_k immersion

Determine whether every graph with minimum degree at least k immerses the complete graph K_k.

Background

Known results give linear average-degree conditions for immersions, and minimum degree k−1 suffices for k ≤ 7, but counterexamples exist for larger k under some strengthened statements. Establishing the minimum-degree threshold exactly at k would resolve a central open problem in immersion theory and imply the chromatic version in many cases.