On the number of upward planar orientations of maximal planar graphs

Fabrizio Frati, Joachim Gudmundsson, Emo Welzl
2014 Theoretical Computer Science  
We consider the problem of determining the maximum and the minimum number of upward planar orientations a maximal planar graph can have. We show that n-vertex maximal planar graphs have at least Ω(n · 1.189 n ) and at most O(n · 4 n ) upward planar orientations. Moreover, there exist n-vertex maximal planar graphs having as few as O(n · 2 n ) upward planar orientations and n-vertex maximal planar graphs having Ω(2.599 n ) upward planar orientations. Support from EuroCores/EuroGiga/ComPoSe SNF 20GG21 134318/1 is acknowledged.
doi:10.1016/j.tcs.2014.04.024 fatcat:gkwwxhkj4vgllne4uukg7u4vxy