The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then adaptively selects a vertex $v$, and adds the edge $uv$ to the graph. For a fixed monotone graph property, the objective of the player is to force the graph to satisfy this property with high probability in as few rounds as possible. In this paper, we investigate the following three properties: containing a complete graph of order $k$, having the chromatic number at least $k$, and not having an independent set of size at least $k$.

翻译：半随机图过程是一个单人游戏，初始时玩家面对一个具有$n$个顶点的空图。每一轮中，独立且均匀随机地呈现一个顶点$u$给玩家，随后玩家自适应地选择顶点$v$，并将边$uv$添加到图中。针对某一固定的单调图性质，玩家的目标是在尽可能少的轮次内，以高概率迫使图满足该性质。本文研究以下三种性质：包含阶数为$k$的完全图、色数至少为$k$、以及不存在大小至少为$k$的独立集。