Isomorphic bisections of cubic graphs

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