On the largest eigenvalue of a sparse random subgraph of the hypercube

Details On the largest eigenvalue of a sparse random subgraph of the hypercube On the largest eigenvalue of a sparse random subgraph of the hypercube

2001-07-31

arxiv.org/abs/math/0107229v1

Mathematics

Combinatorics

Scientific paper

We consider a sparse random subraph of the $n$-cube where each edge appears
independently with small probability $p(n) =O(n^{-1+o(1)})$. In the most
interesting regime when $p(n)$ is not exponentially small we prove that the
largest eigenvalue of the graph is asymtotically equal to the square root of
the maximum degree.

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