Every graph with no $K_7^{=}$ minor is 6-colorable

Zdeněk Dvořák, Sergey Norin, Neil Rahman

The first open case of Hadwiger's conjecture states that every $K_7$-minor-free graph is 6-colorable. We prove that this is the case for $K_7^{=}$-minor-free graphs, where $K_7^{=}$ de…