This paper gives a precise structure theorem for the class of graphs which do not contain $W_4$ as an immersion. This strengthens a previous result of Belmonte et al. that gives a rough description of this class. In fact, we prove a stronger theorem concerning rooted immersions of $W_4$ where one terminal is specified in advance. This stronger result is key in a forthcoming structure theorem for graphs with no $K_{3,3}$ immersion.

中文翻译：

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没有 W 4 浸入的图的结构

本文给出了不包含图类的精确结构定理 ${宽}_4$作为沉浸。这加强了 Belmonte 等人先前的结果。这给出了这个类的粗略描述。事实上，我们证明了一个关于根浸入的更强定理${宽}_4$其中一个终端是提前指定的。这个更强的结果是即将出现的图的结构定理的关键，没有${钾}_{3,3}$ 浸没。