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arxiv: 1402.2806 · v1 · pith:6SEMWQ4Gnew · submitted 2014-02-12 · 🧮 math.CO

Coloration of K₇^--minor free graphs

classification 🧮 math.CO
keywords freeminorcolorablegraphsbeengraphprovedalbar
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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.

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