An algorithm for an 𝓁2-homological test for the planarity of a graph

DOI10.1016/j.akcej.2019.08.013zbMath1471.05101OpenAlexW3047716742MaRDI QIDQ4956221

Elizabeth A. Donovan, Timothy A. Schroeder

Publication date: 1 September 2021

Published in: AKCE International Journal of Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.akcej.2019.08.013

zbMATH Keywords

Coxeter groupplanarityDavis complex\(\ell^2 \)-Betti numbers

Mathematics Subject Classification ID

Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Planar graphs; geometric and topological aspects of graph theory (05C10) Topological methods in group theory (57M07) Graph algorithms (graph-theoretic aspects) (05C85)

Cites Work

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• The \(L^2\)-(co)homology of groups with hierarchies
• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• The \(\ell^2\)-homology of even Coxeter groups.
• Geometrization of 3-dimensional Coxeter orbifolds and Singer's conjecture
• Vanishing theorems and conjectures for the 2-homology of right-angled Coxeter groups
• Introduction to \(\ell_2\)-methods in topology: Reduced \(\ell_2\)-homology, harmonic chains, \(\ell_2\)-Betti numbers
• On almost-planar graphs
• \(L^ 2\)-topological invariants of 3-manifolds
• l²-homology and planar graphs
• On the Cutting Edge: Simplified O(n) Planarity by Edge Addition
• Depth-First Search and Linear Graph Algorithms

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