English

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 nn-vertex planar graph, augments this graph in O(n2)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.

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}
}