A graph drawn on the plane is 2-immersed in the plane if each edge is crossed by at most two other edges. By a proper 2-immersion of a graph we mean a 2-immersion of the graph in the plane such that there is at least one crossing point. We consider the class $\mathcal{T}$ of all finite graphs triangulating the plane such that the graphs have no loops and multiple edges, the vertices have degree 5 and 6 only, and the distance between any two 5-valent vertices is at least 4. In this series of papers we construct graphs of the class $\mathcal{T}$ having no proper 2-immersions. In the present paper we obtain a necessary condition for a graph of the class $\mathcal{T}$ to have a proper 2-immersion. Then we construct a graph of the class $\mathcal{T}$ that does not satisfy the necessary condition thereby obtaining a planar graph having no proper 2-immersions.

如果每条边最多与其他两条边交叉，则绘制在平面上的图形是 2-浸入平面中。图形的适当的2-浸入是指图形在平面中的2-浸入使得至少有一个交叉点。我们考虑类$\mathcal{吨}$ 在所有有限图中对平面进行三角剖分，使得图没有环和多条边，顶点只有度数 5 和 6，并且任意两个 5 价顶点之间的距离至少为 4。 在本系列论文中，我们构造图班级的 $\mathcal{吨}$没有适当的 2 次浸泡。在本文中，我们获得了类图的必要条件$\mathcal{吨}$有一个适当的 2 沉浸。然后我们构造一个类的图$\mathcal{吨}$ 不满足必要条件，从而得到一个没有适当的 2-浸入的平面图。