Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs

04/25/2022

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by   Miriam Goetze, et al.

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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 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.