半随机图过程
Semi-random graph process
摘要：
我们介绍和研究了一种新的半随机多重图过程，描述如下。该过程从$n$顶点上的空图开始。在该过程的每一轮中，图的一个顶点$v$被随机且独立于所有先前的轮均匀地拾取。然后我们选择一个额外的顶点（根据我们选择的策略），并通过边将其连接到$v$。对于各种自然单调递增图形属性$P$，我们证明了严格的上限和下限上的最小（扩展到所有可能的策略集）轮数所需的过程中，以高概率，一个图形，满足$P$。一路上，我们证明了这个过程是足够一般的近似（使用合适的策略）几个研究得很好的随机图模型。
英文摘要：
We introduce and study a novel semi-random multigraph process, described as follows. The process starts with an empty graph on $n$ vertices. In every round of the process, one vertex $v$ of the graph is picked uniformly at random and independently of all previous rounds. We then choose an additional vertex (according to a strategy of our choice) and connect it by an edge to $v$. For various natural monotone increasing graph properties $P$, we prove tight upper and lower bounds on the minimum (extended over the set of all possible strategies) number of rounds required by the process to obtain, with high probability, a graph that satisfies $P$. Along the way, we show that the process is general enough to approximate (using suitable strategies) several well-studied random graph models.
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