A graph drawn on the plane is k-immersed ($k\ge 1$) in the plane if each edge is crossed by at most k other edges. By a proper k-immersion of a graph we mean a k-immersion of the graph in the plane such that there is at least one crossing point. Planar graphs having no proper 1-immersions were constructed before, and it was shown that every connected planar graph has a proper 3-immersion (with the exception of $K_3$ and $K_{1,n}$). There remained an open problem of whether there exist planar graphs having no proper 2-immersions. 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 study properties of graphs of the class $\mathcal{T}$ and properties of proper 2-immersions of the graphs.

在平面上绘制的图形是k浸入的（$克\ge 1$) 在平面中，如果每条边最多与k 条其他边相交。通过一个适当的ķ -浸渍的曲线图的，我们是指一个ķ在平面图中，使得存在至少一个交叉点的-immersion。之前构造了没有适当的 1-浸入的平面图，并且证明了每个连通的平面图都有适当的 3-浸入（除了${钾}_3$ 和 ${钾}_{1,n}$）。是否存在没有适当的 2-浸入的平面图仍然存在一个悬而未决的问题。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，我们研究了类图的性质$\mathcal{吨}$ 和图形的适当 2 浸入的性质。