Lescure–Meyniel–Abu-Khzam–Langston conjecture on chromatic number and clique immersions

Let $G$ be a graph, let $\chi(G)$ denote its chromatic number, and let $K_t$ be the complete graph on $t$ vertices. An $H$-immersion is an injective mapping of $V(H)$ to $V(G)$ together with pairwise edge-disjoint paths in $G$ joining the images of the endpoints of every edge of $H$. Lescure–Meyniel–Abu-Khzam–Langston conjecture. Every graph $G$ with $\chi(G)\geq t$ contains a $K_t$-immersion. The paper presents this as an analogue of Hajós's conjecture; its resolution status is not specified in the supplied text.