On the Largest Eigenvalue of a Random Subgraph of the Hypercube
Abstract
Let G be a random subgraph of the n-cube where each edge appears randomly and independently with probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely λ1(G)= (1+o(1)) max(1/2(G),np), where (G) is the maximum degree of G and o(1) term tends to zero as max (1/2(G), np) tends to infinity.
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