We present a refinement of the classical alteration method for constructing $H$-free graphs: for suitable edge-probabilities $p$, we show that removing all edges in $H$-copies of the binomial random graph $G_{n,p}$ does not significantly change the independence number. This differs from earlier alteration approaches of Erd\H{o}s and Krivelevich, who obtained similar guarantees by removing one edge from each $H$-copy (instead of all of them). We demonstrate the usefulness of our refined alternation method via two applications to online graph Ramsey games, where it enables easier analysis.

翻译：我们提出了经典变型方法的改进，用于构造不含$H$子图的图：对于适当的边概率$p$，我们证明移除二项式随机图$G_{n,p}$中所有$H$副本的边不会显著改变独立数。这与Erdős和Krivelevich早期的变型方法不同，他们通过移除每个$H$副本中的一条边（而非全部边）获得了类似的保证。我们通过在线图拉姆齐博弈的两个应用展示了改进变型方法的实用性，该方法使得分析更加简便。