论文标题
$ 8 $ -Contraction-Contractication图的属性，没有$ k_7 $ binor
Properties of $8$-contraction-critical graphs with no $K_7$ minor
论文作者
论文摘要
在著名的哈德威格（Hadwiger）的猜想中，我们研究了$ 8 $ contraction-Contraction-Contraction-Contraction-Contrication-thake的属性；我们证明，每$ 8 $ -Contraction-Contraction-Contraction-Contrical图形最多都有一个顶点$ 8 $，其中图$ g $是$ 8 $ -Contraction-Contical-Contraction-Contical-Contraction-Contractical-Contractical-Contraction-Contraction-Contractical-G $不是$ 7 $ -Colorable-colorableable-colorable，但$ G $的每一个适当的少数$ G $ is $ 7 $ - 颜色$ -Colorable。这是我们努力证明，没有$ k_7 $ binor的每张图的努力是$ 7 $ - 油腻的，这仍然是开放的。
Motivated by the famous Hadwiger's Conjecture, we study the properties of $8$-contraction-critical graphs with no $K_7$ minor; we prove that every $8$-contraction-critical graph with no $K_7$ minor has at most one vertex of degree $8$, where a graph $G$ is $8$-contraction-critical if $G$ is not $7$-colorable but every proper minor of $G$ is $7$-colorable. This is one step in our effort to prove that every graph with no $K_7$ minor is $7$-colorable, which remains open.
