Geodesic
The (3,1)-ordering for 4-connected planar triangulations
Journal of Graph Algorithms and Applications, Tome 20 (2016) no. 2, pp. 347-362.

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Canonical orderings of planar graphs have frequently been used in graph drawing and other graph algorithms. In this paper we introduce the notion of an $(r,s)$-canonical order, which unifies many of the existing variants of canonical orderings. We then show that $(3,1)$-canonical ordering for 4-connected triangulations always exist; to our knowledge this variant of canonical ordering was not previously known. We use it to give much simpler proofs of two previously known graph drawing results for 4-connected planar triangulations, namely, rectangular duals and rectangle-of-influence drawings.
DOI : 10.7155/jgaa.00396
Keywords: canonical ordering, planar graph, graph drawing, 4-connected planar graph, rectangular dual, rectangle-of-influence drawing 
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Therese Biedl; Martin Derka. The (3,1)-ordering for 4-connected planar triangulations. Journal of Graph Algorithms and Applications, Tome 20 (2016) no. 2, pp. 347-362. doi : 10.7155/jgaa.00396. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00396/

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