A binary labelling for plane Laman graphs and quadrangulations
Clemens Huemer, Sarah Kappes · 2006
We present binary labelings for the angles of quadrangulations and plane Laman graphs, which are in analogy with Schnyder labelings for triangulations [W. Schnyder, Proc. 1st ACM-SIAM Symposium on Discrete Algorithms, 1990] and imply a special tree decomposition for quadrangulations. In particular, we show how to embed quadrangulations on a 2-book, so that each page contains a non-crossing alternating tree.