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Exploiting the techniques introduced for proving that straight-line upward RAC drawings of upward planar digraphs may require exponential area, we also show that there exist
A simple method to draw a DAG by applying upward planarization consists of using Sugiyama’s coordinate assignment phase for drawing the upward planar rep- resentation, where we use
Also using the identities given in section 1, we derive some new identities for Fibonacci and Lucas numbers.. Let us give them in the
We calculate here both exact and asymptotic formulas for the number of regions enclosed by the edges of a regular drawing of the complete bipartite graph K
The regular drawing of the complete bipartite graph K n,n produces a striking pat- tern comprising simple and multiple crossings.. We compute the number c ( n ) of cross- ings and
These results are used to characterize all extremal weighted trees with the largest p -Laplacian spectral radius among all weighted trees with a given degree sequence and a
The other reason why LERWs are studied is that they are closely related to certain models in statistical physics like the uniform spanning tree (through Wilson’s algorithm which
In positive genus, Chapuy, Marcus, and Schaeffer [ 6 ] extended the bijective approaches known for the planar case, leading Chapuy [ 5 ] to establish the convergence of the
