Following in the spirit of the Hadwiger and Hajós conjectures, Abu-Khzam and Langston have conjectured that every ▫$k$▫-chromatic graph contains an immersion of ▫$K_k$▫. They proved this for ▫$k \le ...4$▫. Here we make the stronger conjecture that every simple graph of minimum degree ▫$k-1$▫ contains an immersion of ▫$K_{k}$▫. We prove that this conjecture holds for every ▫$k \le 7$▫.
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