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Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs

Authors Miriam Goetze , Paul Jungeblut , Torsten Ueckerdt

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Miriam Goetze
  • Karlsruhe Institute of Technology, Germany
Paul Jungeblut
  • Karlsruhe Institute of Technology, Germany
Torsten Ueckerdt
  • Karlsruhe Institute of Technology, Germany

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Miriam Goetze, Paul Jungeblut, and Torsten Ueckerdt. Efficient Recognition of Subgraphs of Planar Cubic Bridgeless Graphs. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 62:1-62:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ESA.2022.62

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(n²) steps to a planar cubic bridgeless supergraph, or decides that no such augmentation is possible. The main tools involve the Generalized (Anti)factor-problem for the fixed embedding case, and SPQR-trees for the variable embedding case.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • edge colorings
  • planar graphs
  • cubic graphs
  • generalized factors
  • SPQR-tree

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