We construct an infinite family of counterexamples to Thomassen’s conjecture that the vertices of every 3-connected, cubic graph on at least 8 vertices can be colored blue and red such that the blue subgraph has maximum degree at most 1 and the red subgraph minimum degree at least 1 and contains no path on 4 vertices.

中文翻译：

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Thomassen关于三次图分解的猜想的反例

我们为 Thomassen 的猜想构建了一个无限的反例族，即至少 8 个顶点上的每个 3-连通三次图的顶点可以被着色为蓝色和红色，这样蓝色子图的最大度数最多为 1，红色子图的最小度数为至少 1 个并且不包含 4 个顶点上的路径。