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DOI: 10.7155/jgaa.00555
On Area-Universal Quadrangulations
Vol. 25, no. 1, pp. 171-193, 2021. Regular paper.
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.
This work is licensed under the terms of the CC-BY license.
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Submitted: July 2020.
Reviewed: October 2020.
Revised: October 2020.
Accepted: January 2021.
Final: January 2021.
Published: January 2021.
Communicated by
Seok-Hee Hong
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