A k-bisection of a graph is a partition of the vertices in two classes whose cardinalities differ of at most one and such that the subgraphs induced by each class are acyclic with all connected components of order at most k. Esperet, Tarsi and the second author proved in 2017 that every simple cubic graph admits a 3-bisection. Recently, Cui and Liu extended that result to the class of simple subcubic graphs. Their proof is an adaptation of the quite long proof of the cubic case to the subcubic one. Here, we propose an easier proof of a slightly stronger result. Indeed, starting from the result for simple cubic graphs, we prove the existence of a 3-bisection for all cubic graphs (also admitting parallel edges). Then we prove the same result for the larger class of subcubic graphs as an easy corollary.

图的k-等分是两类顶点的分割，其基数最多相差一个，因此每个类导出的子图都是无环的，所有连通的阶次最多为k。Esperet，Tarsi和第二作者在2017年证明，每个简单的立方图都允许一个三等分。最近，崔和刘将其结果扩展到简单的亚三次图类。他们的证明是三次案例的相当长的证明与次三次案例的适应。在这里，我们提出一个更简单的证据来证明结果略强。确实，从简单三次方图的结果开始，我们证明了所有三次方图都存在一个三等分（也允许平行边）。然后，我们证明了对于较大类次立方图的相同结果是一个简单的推论。