This paper deals with the maximum independent set (M.I.S.) problem, also known as the stable set problem. The \textit{basic} mathematical programming model that captures this problem is an Integer Program (I.P.) with zero-one variables and only the \textit{edge inequalities}. We present an enhanced I.P. by adding a polynomial number of linear constraints, known as \textit{valid inequalities}; this new model is still polynomial in the number of vertices in the graph. We carried out computational testing of the Linear Relaxation of the new I.P. ~We tested about 5000 instances of randomly generated (and connected) graphs with up to 40 vertices. In each of these instances, the Linear Relaxation returned an optimal solution with (i) every variable having an integer value, and (ii) the optimal solution value of the Linear Relaxation was the same as that of the original (\textit{basic}) I.P.

翻译：本文涉及最大的独立设置问题( M. I. S. ), 也称为稳定设置问题 。 记录这一问题的 \ textit{ basic} 数学编程模型是一个包含零一变量的整数程序( I. P. ), 仅包含 \ textit{ gether evenity } 。 我们展示了一个强化的一P. P., 方法是添加一个线性约束的多数值, 称为\ textit{ valid equal } ; 这个新模型仍然是图中脊椎数的多元值 。 我们对新 I. P. ~ 我们测试了5000 个随机生成( 连接) 的图和 40 个顶脊椎的整数 。 在每种情况下, 线性放松都返回了一个最佳的解决方案, (i) 每个具有整数的变量, 和 (ii) 线性放松的最佳解决方案值与原始的(\ textit{ { { } I. P.