Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs
Data Structures and Algorithms
2022-07-18 v2 Combinatorics
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 -vertex planar graph, augments this graph in 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.
Keywords
Cite
@article{arxiv.2204.11750,
title = {Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs},
author = {Miriam Goetze and Paul Jungeblut and Torsten Ueckerdt},
journal= {arXiv preprint arXiv:2204.11750},
year = {2022}
}