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.
Cite
@article{arxiv.1908.10457,
title = {Clique immersion in graph products},
author = {Karen L. Collins and Megan E. Heenehan and Jessica McDonald},
journal= {arXiv preprint arXiv:1908.10457},
year = {2019}
}