Abstract
The generation of a random triangle-saturated graph via the triangle-free process has been studied extensively. In this short note our aim is to introduce an analogous process in the hypercube. Specifically, we consider the
Q
2
-free process in
Q
d
and the random subgraph of
Q
d
it generates. Our main result is that with high probability the graph resulting from this process has at least
c
d
2
/
3
2
d
edges. We also discuss a heuristic argument based on the differential equations method which suggests a stronger conjecture, and discuss the issues with making this rigorous. We conclude with some open questions related to this process.
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