On the Largest Eigenvalue of a Random Subgraph of the Hypercube
نویسندگان
چکیده
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 ofG and theo(1) term tends to zero as max( 1/2(G), np) tends to infinity.
منابع مشابه
Se p 20 02 On the largest eigenvalue of a random subgraph of the hypercube ∗
Let G be a random subgraph of the n-cube where each edge appears randomly and independently with small probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely λ1(G) = (1 + o(1))max ( ∆(G), np ) , where ∆(G) is the maximum degree of G and the o(1) term tends to zero as max(∆(G), np) tends to infinity.
متن کاملFe b 20 03 On the largest eigenvalue of a random subgraph of the hypercube ∗
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 ( ∆(G), np ) , where ∆(G) is the maximum degree of G and the o(1) term tends to zero as max(∆(G), np) tends to infinity.
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