Testing subgraphs in large graphs

Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least n2 edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f( , H)nh copies of H. We show that the largest possible function f( , H) is polynomial in if and only if H is bipartite. This implies that there is a one-sided error property tester for checking H-freeness, whose query complexity is polynomial in 1/ , if and only if H is bipartite.

• Type: Journal
• Year: 2002
• Where: RSA
• Authors: Noga Alon
• Keywords: Fixed Graph, Largest Possible Function, One-sided Error Property, RSA 2002