Small Subgraphs in the Trace of a Random Walk
نویسندگان
چکیده
We consider the combinatorial properties of the trace of a random walk on the complete graph and on the random graph G(n, p). In particular, we study the appearance of a fixed subgraph in the trace. We prove that for a subgraph containing a cycle, the threshold for its appearance in the trace of a random walk of length m is essentially equal to the threshold for its appearance in the random graph drawn from G(n,m). In the case where the base graph is the complete graph, we show that a fixed forest appears in the trace typically much earlier than it appears in G(n,m).
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عنوان ژورنال:
- Electr. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2017