Geodesic
On Area-Universal Quadrangulations
Journal of graph algorithms and applications, Tome 25 (2021) no. 1, pp. 171-193 Cet article a éte moissonné depuis la source Journal of Graph Algorythms and Applications website

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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. 
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     title = {On {Area-Universal} {Quadrangulations}},
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William Evans; Stefan Felsner; Linda Kleist; Stephen Kobourov. On Area-Universal Quadrangulations. Journal of graph algorithms and applications, Tome 25 (2021) no. 1, pp. 171-193. doi: 10.7155/jgaa.00555

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