The triangle‐free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle‐free graph at which the triangle‐free process terminates. We also bound the independence number of this graph, which gives an improved lower bound on the Ramsey numbers R(3, t): we show , which is within a 4 + o(1) factor of the best known upper bound. Our improvement on previous analyses of this process exploits the self‐correcting nature of key statistics of the process. Furthermore, we determine which bounded size subgraphs are likely to appear in the maximal triangle‐free graph produced by the triangle‐free process: they are precisely those triangle‐free graphs with density at most 2.

中文翻译：

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无三角过程的动态集中

无三角形的过程从n个顶点上的空图开始，然后迭代地添加随机地均匀选择的边，但要遵守没有形成三角形的约束。我们确定无三角过程终止的最大无三角图中边的渐近数。我们还限制了该图的独立数，这使Ramsey数R（3，  t）的下限得到了改进：我们显示，它在4 + o以内 （1）最著名的上限的因子。我们对该过程的先前分析的改进利用了过程关键统计数据的自校正特性。此外，我们确定在无三角过程产生的最大无三角图中，哪些有界尺寸子图可能出现：它们恰好是那些密度最高为2的无三角图。