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arXiv · 2204.11750

Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs

Miriam Goetze·Paul Jungeblut·Torsten Ueckerdt
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Abstract

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 Generalized Antifactor-problem for the fixed embedding case, and SPQR-trees for the variable embedding case.

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Miriam Goetze, Paul Jungeblut, Torsten Ueckerdt. 2022-04-25. Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs. https://arxiv.org/abs/2204.11750

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