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Testing subgraphs in large graphs

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1 Author(s)
N. Alon ; Raymond & Beverly Sackler Fac. of Exact Sci., Tel Aviv Univ., Israel

Let H be a fixed graph with h vertices, let G be a graph on n vertices and suppose that at least εn2 edges have to be deleted from it to make it H-free. It is known that in this case G contains at least f (ε, H)nh copies of H. We show that the largest possible function f (ε, H) is polynomial in ε 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/ε, if and only if H is bipartite.

Published in:

Foundations of Computer Science, 2001. Proceedings. 42nd IEEE Symposium on

Date of Conference:

8-11 Oct. 2001