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).
| Original language | English GB |
|---|---|
| Article number | #P1.28 |
| Journal | Electronic Journal of Combinatorics |
| Volume | 24 |
| Issue number | 1 |
| DOIs | |
| State | Published - 17 Feb 2017 |
Keywords
- Random graph
- Random walk
- Small subgraph
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics
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