色多项式的逼近
Approximating the Chromatic Polynomial
摘要：
色多项式是图论和统计物理中的重要对象，但由于计算困难，它们的研究仅限于小的，高度结构化的或非常稀疏的图。我们已经设计并实现了两个算法，近似的色多项式$P(G,x)$的系数，其中$P(G,k)$是正确的$k$着色的图$G$的$k\in\mathbb{N}$的数量。我们的算法是基于Knuth的方法，估计搜索树的顺序。我们比较我们的结果，真正的色多项式在几个已知的情况下，并比较我们的误差与以前的近似算法。
英文摘要：
Chromatic polynomials are important objects in graph theory and statistical physics, but as a result of computational difficulties, their study is limited to graphs that are small, highly structured, or very sparse. We have devised and implemented two algorithms that approximate the coefficients of the chromatic polynomial $P(G,x)$, where $P(G,k)$ is the number of proper $k$-colorings of a graph $G$ for $k\in\mathbb{N}$. Our algorithm is based on a method of Knuth that estimates the order of a search tree. We compare our results to the true chromatic polynomial in several known cases, and compare our error with previous approximation algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
