A caterpillar is either a $K_2$ or a tree on at least 3 vertices such that deleting its leaves we obtain a path of order at least 1. Given a simple undirected graph $G=(V,E)$, a caterpillar factor of G is a set of caterpillar subgraphs of G such that each vertex $v\in V$ belongs to exactly one of them. A caterpillar factor F is internally even if every vertex of degree ${\mathrm{deg}}_F(v)\ge 2$ has an even degree; F is odd if ${\mathrm{deg}}_F(v)$ is odd for every $v\in V(G)$. We present a linear-time algorithm that decides whether a tree admits an internally even caterpillar factor and, on the other hand, we prove that the decision problem is NP-complete on the class of planar bipartite graphs. For the odd caterpillar factor problem, we obtain similar results. It can be decided in linear time over the class of trees, but the problem is NP-complete on the class of bipartite graphs.

甲毛虫或者是一个${ķ}_2$ 或至少3个顶点上的树，以便删除其叶子，我们可获得至少1的有序路径。给定一个简单的无向图 $G=（V，Ë）$中，毛虫因子的ģ是一组履带子图G ^，使得每个顶点$v\in V$完全属于其中之一。即使度数的每个顶点，毛虫因子F也在内部${\mathrm{度}}_F（v）\ge 2$程度均匀 如果F是奇数${\mathrm{度}}_F（v）$ 每个都是奇怪的 $v\in V（G）$。我们提出一种线性时间算法，该算法确定一棵树是否允许内部均匀的毛毛虫因子，另一方面，我们证明了该决策问题在平面二部图类上是NP完全的。对于奇数毛毛虫因子问题，我们获得了相似的结果。可以在树的类上以线性时间来确定，但是问题是二部图类上的NP完全。