排序方式: 共有1条查询结果,搜索用时 15 毫秒
1
1.
Nicolas Bonichon Cyril Gavoille Nicolas Hanusse Dominique Poulalhon Gilles Schaeffer 《Graphs and Combinatorics》2006,22(2):185-202
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 2αn+O(logn), 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, log2p(n)≤4.91n.
The result is then used to show that asymptotically almost all (labeled or unlabeled), (connected or not) planar graphs with
n nodes have between 1.85n and 2.44n edges.
Finally we obtain as an outcome of our combinatorial analysis an explicit linear-time encoding algorithm for unlabeled planar
graphs using, in the worst-case, a rate of 4.91 bits per node and of 2.82 bits per edge. 相似文献
1