A characterization of easily testable induced subgraphs

Let H be a fixed graph on h vertices. We say that a graph G is induced H-free if it does not contain any induced copy of H. Let G be a graph on n vertices and suppose that at least n2 edges have to be added to or removed from it in order to make it induced H-free. It was shown in [5] that in this case G contains at least f( , h)nh induced copies of H, where 1/f( , h) is an extremely fast growing function in 1/ , that is independent of n. As a consequence, it follows that for every H, testing induced H-freeness with one-sided error has query complexity independent of n. A natural question, raised by the first author in [1], is to decide for which graphs H the function 1/f( , H) can be bounded from above by a polynomial in 1/ . An equivalent question is for which graphs H, can one design a one-sided error property tester for testing induced Hfreeness, whose query complexity is polynomial in 1/ . We settle this question almost completely by showing that, quite surprisingly, for any graph...

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Noga Alon, Asaf Shapira
• Keywords: Algorithms, H)nh Induced Copies, One-sided Error, SODA 2004, Testing Induced H-freeness