  The analog of Hadwiger's conjecture for the immersion relation states that
every graph $G$ contains an immersion of $K_{\chi(G)}$. For graphs with
independence number 2, this is equivalent to stating that every such $n$-vertex
graph contains an immersion of $K_{\lceil n/2 \rceil}$. We show that every
$n$-vertex graph with independence number 2 contains every complete bipartite
graph on $\lceil n/2 \rceil$ vertices as an immersion.
