Coloration of $K_7^{-}$-minor free graphs

Abstract

Hadwiger's conjecture says that every $K_t$-minor free graph is $(t-1)$-colorable. This problem has been proved for $t\le 6$ but remains open for $t\ge 7$. $K_7$-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.

11 pages, 1 figure

References in corpus (1)

• On triangles in K_r-minor free graphs