Abstract
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 , 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 . 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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