Abstract
Let G,H be graphs and G⁎H represent a particular graph product of G and H. We define im(G) to be the largest t such that G has a Kt-immersion and ask: given im(G)=t and im(H)=r, how large is im(G⁎H)? Best possible lower bounds are provided when ⁎ is the Cartesian or lexicographic product, and a conjecture is offered for each of the direct and strong products, along with some partial results.
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