随机完全图中某些子图的概率分布极限定理

The Limit Theorem of Probability Distribution of Certain Subgraphs in Random Complete Graph

设k(n,l,t)表示随机l边着色完全图K_n中单色完全子图K_l的个数.c(n,l)表示随机竞赛图T_n中1圈的个数.用k(n,l,t)或c(n,l),则■的分布趋于标准正态分布。

Let k(n,l, t) be the number of monochromatic complete subgraph K_l in random t-edge-calored complete graph K_n, c(n, l) be the munber of l-cycle in random tournament T_n Dcnote k(n, l, t) or c(n,l) by ξ_n,then the distribution of (ξ_n-E(ξ_n) tends to the normal distribution with zero mean and unit variance.