列舉組合物件在組合數學中一直都是重要的研究項目，而我們稱隨機產生組合物件的演算法為取樣。取樣在電腦科學中有很多的應用，像是程式正確性的測試等等，而且數學家也可以利用取樣的結果去驗證一些數學性質。
我們利用蒙地卡羅馬可夫鍊的方法設計出k 連通圖形的取樣方法，而我們可以證明出此方法可以近似均勻分布的產生k連通圖形，並且我們也證明了這演算法是快速收斂的。

Enumerating combinatorial objects is an important research topic in combinatorics. Algorithms for random generating combinatorial objects are called sampling. Sampling has many applications in computer science, for example program testing. Mathematicians
can use sampling to verify combinatorial property.
We developed a simple algorithm to sample k-connected graphs based on Markov Chain Monte Carlo method. This algorithm generates graphs at approximately uniform distribution, and we prove it is rapidly mixing

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