Coloration of $K_7^-$-minor free graphs

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 & Gonçalves, 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.

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