The weight of an edge e is the degree-sum of its end-vertices. An edge $e=uv$ is an $(i,j)$-edge if $\text{deg}(u)\le i$ and $\text{deg}(v)\le j$. In 1955, Kotzig proved that every 3-connected planar graph contains an edge of weight at most 13. Later, Borodin extended this result to the class of simple planar graphs with minimum degree at least 3. If we consider the class of plane graphs with minimum degree two, the existence of an edge with small weight can be proved under various conditions (for example girth at least five or bounded number of adjacent vertices of degree two). In this paper we investigate the structure of edges in plane graphs with prescribed dual edge weight what is the minimum sum of degrees of two faces sharing an edge. We prove that every plane graph with minimum degree two and dual edge weight at least $w^{⁎}$ contains an edge of type $(2,10)$ or $(3,4)$ if $w^{⁎}=9$, $(2,10)$ or $(3,3)$ if $w^{⁎}=10$, $(2,6)$ or $(3,3)$ if $w^{⁎}\in \{11,12,13\}$, $(2,6)$ if $w^{⁎}=14$, and $(2,4)$ if $w^{⁎}\ge 15$. Moreover, all the bounds are the best possible.

边缘e的权重是其最终顶点的度和。优势$Ë=üv$ 是一个 $（\mathrm{一世}，Ĵ）$-边缘如果 $\text{度}（ü）\le \mathrm{一世}$ 和 $\text{度}（v）\le Ĵ$。1955年，科茨格（Kotzig）证明，每个3连通平面图最多包含13个权重边。后来，鲍罗丁（Bordinin）将结果扩展到最小度至少为3的简单平面图类。最小二阶，可以在各种条件下证明具有较小权重的边的存在（例如，周长至少为五或二阶的相邻顶点的边界个数）。在本文中，我们研究了具有指定双边权重的平面图中的边结构，该权重是指共享一条边的两个面的最小度数之和。我们证明每个平面图的最小二度和双边权重至少$w^{⁎}$ 包含类型的边 $（\mathrm{2个}，10）$ 或者 $（3，4）$ 如果 $w^{⁎}=9$， $（\mathrm{2个}，10）$ 或者 $（3，3）$ 如果 $w^{⁎}=10$， $（\mathrm{2个}，6）$ 或者 $（3，3）$ 如果 $w^{⁎}\in \{11，12，13\}$， $（\mathrm{2个}，6）$ 如果 $w^{⁎}=14$， 和 $（\mathrm{2个}，4）$ 如果 $w^{⁎}\ge 15$。而且，所有范围都是最好的。