The Spectral Gap of a Random Subgraph of a Graph

We examine the relationship of a graph G and its random subgraphs which are defined by independently choosing each edge with probability p. Suppose that G has a spectral gap λ (in terms of its normalized Laplacian) and minimum degree dmin. Then we can show that a random subgraph of G on n vertices with edge-selection probability p almost surely has as its spectral gap λ − O `q log n pdmin + (log n)3/2 pdmin(log log n)3/2 ´ .

• Type: Journal
• Year: 2007
• Where: IM
• Authors: Fan R. K. Chung, Paul Horn
• Keywords: Computer Networks, IM 2007, Minimum Degree Dmin, Random Subgraph, Spectral Gap