论文标题
列举平面图和地图的枚举
Enumeration of chordal planar graphs and maps
论文作者
论文摘要
我们确定具有$ n $顶点的标记的和弦平面图的数量，该图是$ c_1 \ cdot n^{ - 5/5/2}γ^n n！$，用于常量$ C_1> 0 $和$γ\ \ $ c_1> 0 $ and $γ\ \ \ \ump。我们还确定了用$ n $边缘的扎根简单的和弦平面映射的数量，$ n $边缘是$ c_2 n^{ - 3/2}δ^n $，其中$δ= 1/σ= 1/σ\约6.40375 $，而$σ$是12 $的12 $。和弦平面图（或地图）是一个亚临界类别的自然示例，其中3个连接图的类相对较丰富。三个连接的成员是cont弦的三角形，从$ k_4 $开始获得的成员是反复添加与现有三角形面相邻的顶点。
We determine the number of labelled chordal planar graphs with $n$ vertices, which is asymptotically $c_1\cdot n^{-5/2} γ^n n!$ for a constant $c_1>0$ and $γ\approx 11.89235$. We also determine the number of rooted simple chordal planar maps with $n$ edges, which is asymptotically $c_2 n^{-3/2} δ^n$, where $δ= 1/σ\approx 6.40375$, and $σ$ is an algebraic number of degree 12. The proofs are based on combinatorial decompositions and singularity analysis. Chordal planar graphs (or maps) are a natural example of a subcritical class of graphs in which the class of 3-connected graphs is relatively rich. The 3-connected members are precisely chordal triangulations, those obtained starting from $K_4$ by repeatedly adding vertices adjacent to an existing triangular face.
