Isomorphic Bisections of Cubic Graphs

TL;DR

This paper proves Ando's conjecture that all large connected cubic graphs can be partitioned into two isomorphic induced subgraphs, using probabilistic and recoloring techniques.

Contribution

It establishes the conjecture for large connected cubic graphs, advancing understanding of graph isomorphism and partitioning.

Findings

Proves Ando's conjecture for large connected cubic graphs.

Uses probabilistic methods and recoloring arguments.

Contributes to graph partitioning theory.

Abstract

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.