AffiliationUniversity of Arizona
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CitationEvans, W. S., Felsner, S., Kleist, L., & Kobourov, S. G. (2021). On Area-Universal Quadrangulations. J. Graph Algorithms Appl., 25(1), 171-193.
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AbstractWe 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. © 2021, Brown University. All rights reserved.
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Except where otherwise noted, this item's license is described as Copyright © 2021 The authors. This work is licensed under the terms of the CC-BY license.