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arXiv · 1605.04585

Small subgraphs in the trace of a random walk

Michael Krivelevich·Peleg Michaeli
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Abstract

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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Michael Krivelevich, Peleg Michaeli. 2016-11-22. Small subgraphs in the trace of a random walk. https://doi.org/10.37236/6169

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