We present a construction of two infinite graphs G1 and G2, and of an infinite set f of graphs such that f is an antichain with respect to the immersion relation and, for each graph G in f, both G1 and G2 are subgraphs of G, but no graph properly immersed in G admits an immersion of G1 and of G2. This shows that the class of infinite graphs ordered by the immersion relation does not have the finite intertwine property.
Publication Source (Journal or Book title)
Journal of Graph Theory
Barnes, M., & Oporowski, B. (2019). A note on immersion intertwines of infinite graphs. Journal of Graph Theory, 92 (1), 57-62. https://doi.org/10.1002/jgt.22440