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.
|Number of pages||8|
|Journal||Annual Symposium on Foundations of Computer Science - Proceedings|
|State||Published - 2001|
|Event||42nd Annual Symposium on Foundations of Computer Science - Las Vegas, NV, United States|
Duration: 14 Oct 2001 → 17 Oct 2001