On the Number of Upward Planar Orientations of Maximal Planar Graphs
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.
KeywordsDirected Graph Planar Graph Internal Vertex Outer Face Internal Edge
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