On area-universal quadrangulations

William Evans, Stefan Felsner, Linda Kleist, Stephen Kobourov

Research output: Contribution to journalArticlepeer-review

Abstract

We study drawings of plane quadrangulations such that every inner face realizes a prescribed area. A plane graph is area-universal if for every assignment of non-negative weights to the inner faces, there exists a straight-line drawing such that the area of each inner face equals the weight of the face. It has been conjectured that all plane quadrangulations are area-universal. We develop methods to prove area-universality via reduction to the area-universality of related graphs. This allows us to establish area-universality for large classes of plane quadrangulations. In particular, our methods are strong enough to prove area-universality of all plane quadrangulations with up to 13 vertices.

Original languageEnglish (US)
Pages (from-to)171-193
Number of pages23
JournalJournal of Graph Algorithms and Applications
Volume25
Issue number1
DOIs
StatePublished - 2021

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Computer Science Applications
  • Geometry and Topology
  • Computational Theory and Mathematics

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