Graph partitioning, or the dividing of a graph into two or more parts based on certain conditions, arises naturally throughout discrete mathematics, and problems of this kind have been studied extensively. In the 1990s, Ando conjectured that the vertices of every cubic graph can be partitioned into two parts that induce isomorphic subgraphs. Using probabilistic methods together with delicate recolouring arguments, we prove Ando's conjecture for large connected graphs.

中文翻译：

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三次图的同构二等分

图划分，或基于特定条件将图划分为两个或多个部分，在离散数学中自然出现，此类问题已被广泛研究。在 1990 年代，Ando 推测每个三次图的顶点都可以分为两部分，从而产生同构子图。使用概率方法和微妙的重新着色参数，我们证明了大型连通图的 Ando 猜想。