Lescure–Meyniel and Abu-Khzam–Langston immersion coloring conjecture

Let $t$ be a positive integer. For a graph $H$, an $H$-immersion is a graph isomorphic to a graph obtained from a subgraph by repeatedly splitting off pairs of edges with a common end and deleting isolated vertices. A graph is properly $t$-colorable if its vertices can be partitioned into $t$ edgeless induced subgraphs. Immersion coloring conjecture. For every positive integer $t$, every graph with no $K_{t+1}$-immersion is properly $t$-colorable. This is the immersion analogue of Hadwiger's conjecture, independently proposed by Lescure and Meyniel and by Abu-Khzam and Langston; the source presents it as an open problem.