Strong-product immersion conjecture

Let $G$ and $H$ be graphs, and write $\operatorname{im}(G)=t$ and $\operatorname{im}(H)=r$. Strong-product immersion conjecture. Then

$$\operatorname{im}(G\boxtimes H)\geq tr.$$

This conjecture is motivated by the identity $K_t\boxtimes K_r=K_{tr}$ and the resulting immersion number of the strong product of complete graphs; the paper presents it as an unresolved conjecture.