It follows from the work of Tait and the Four-Color-Theorem that a planar cubic graph is 3-edge-colorable if and only if it contains no bridge. We consider the question of which planar graphs are subgraphs of planar cubic bridgeless graphs, and hence 3-edge-colorable. We provide an efficient recognition algorithm that given an $n$-vertex planar graph, augments this graph in $\mathcal{O}(n^2)$ steps to a planar cubic bridgeless supergraph, or decides that no such augmentation is possible. The main tools involve the GeneralizedFactor-problem for the fixed embedding case, and SPQR-trees for the variable embedding case.

翻译：根据泰特和四色理论的工作, 平面立方图只有在没有桥梁的情况下才具有3- 亮色。 我们考虑的是哪些平面图是平面立方图的子图, 因而是3色的。 我们提供了一个有效的识别算法, 以美元为单位, 以负平面平面图为单位, 以$\ mathcal{O}( n2) 为单位, 将这个图添加到平面立方体无桥超强图上, 或决定不可能进行这种增强 。 主要工具涉及固定嵌入的通用方程式问题, 以及变量嵌入的 SPQR 树 。