  Hadwiger's conjecture says that every $K_t$-minor free graph is $(t -
1)$-colorable. This problem has been proved for $t \leq 6$ but remains open for
$t \geq 7$. $K_7$-minor free graphs have been proved to be $8$-colorable (Albar
& Gon\c{c}alves, 2013). We prove here that $K_7^-$-minor free graphs are
$7$-colorable, where $K_7^-$ is the graph obtained from $K_7$ by removing one
edge.

Combinatorics