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Planar Graphs, via Well-Orderly Maps and Trees
[chapter]

2004
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Lecture Notes in Computer Science
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The family of well-orderly maps is a family of planar maps with the property that every connected planar graph has at least one plane embedding which is a well-orderly map. We show that the number of well-orderly maps with n nodes is at most 2 αn+O(log n) , where α ≈ 4.91. A direct consequence of this is a new upper bound on the number p(n) of unlabeled planar graphs with n nodes, log 2 p(n) 4.91n. The result is then used to show that asymptotically almost all (labeled or unlabeled), (connected

doi:10.1007/978-3-540-30559-0_23
fatcat:hwqgggbsibabvfbwjqqmpfiaf4