论文标题
Tutte多项式和随机聚类的随机近似方案，在细胞和超密集图中
Randomized Approximation Schemes for the Tutte Polynomial and Random Clustering in Subdense and Superdense Graphs
论文作者
论文摘要
扩展了Alon的作品，Frieze Abnd Welsh的工作，我们表明，有一些随机的多项式近似时间近似方案用于计算tutte多项式的细分图，并具有最小的节点度，$ω\ left（\ frac {n} {N}在随机群集模型中，分区功能$ z $具有均匀边缘概率的$ z $，并且相关的分布$λ（a），\：a \ subseteq e $每当基础图$ g =（v，e）$ is $ c \ cdot \ cdot \ cdot \ cdot \ frac {n} {n} {\ sqrt {\ sqrt {\ sqrt {\ log log（n）} $时，在带有节点度$ n-o（n）$的超密集情况下，我们表明tutte polyenmial $ t_g（x，y）$渐近地等于$ q =（x-1）（y-1）$。此外，我们简要讨论了在$（α，β）$ - 功率定律图的情况下近似$ z $的问题。
Extending the work of Alon, Frieze abnd Welsh, we show that there are randomized polynomial time approximation schemes for computing the Tutte polynomial in subdense graphs with an minimal node degree of $Ω\left ( \frac{n}{\sqrt{\log n}}\right )$ . The same holds for the partition function $Z$ in the random cluster model with uniform edge probabilities and for the associated distribution $λ(A),\: A \subseteq E$ whenever the underlying graph $G=(V,E)$ is $c\cdot\frac{n}{\sqrt{\log (n)}}$-subdense. In the superdense case with node degrees $n-o(n)$, we show that the Tutte polynomial $T_G(x,y)$ is asymptotically equal to $Q=(x-1)(y-1)$. Moreover, we briefly discuss the problem of approximating $Z$ in the case of $(α, β)$-power law graphs.
