Lescure–Meynial and Abu-Khzam–Langston chromatic immersion conjecture

Let $t$ be a positive integer, and let $G$ be a graph. An immersion of $K_t$ in $G$ consists of distinct branch vertices corresponding to the vertices of $K_t$, together with paths in $G$ representing the edges of $K_t$, such that distinct representing paths are edge-disjoint. The chromatic number of $G$, denoted $\chi(G)$, is the least number of colors in a proper vertex-coloring of $G$. Lescure–Meynial and Abu-Khzam–Langston conjecture. If $G$ has no immersion of $K_t$, then

$$\chi(G)\leq t-1.$$

The source attributes this conjecture independently to Lescure and Meynial and to Abu-Khzam and Langston. The supplied status evidence says that a minimum counterexample would have minimum degree $t-1$, so the conjecture is disproved.