Sciweavers

STOC
2003
ACM

Testing subgraphs in directed graphs

14 years 11 months ago
Testing subgraphs in directed graphs
Let H be a fixed directed graph on h vertices, let G be a directed graph on n vertices and suppose that at least n2 edges have to be deleted from it to make it H-free. We show that in this case G contains at least f( , H)nh copies of H. This is proved by establishing a directed version of Szemer?edi's regularity lemma, and implies that for every H there is a one-sided error property tester whose query complexity is bounded by a function of only for testing the property PH of being H-free. As is common with applications of the undirected regularity lemma, here too the function 1/f( , H) is an extremely fast growing function in . We therefore further prove a precise characterization of all the digraphs H, for which f( , H) has a polynomial dependency on . This implies a characterization of all the digraphs H, for which the property of being H-free has a one sided error property tester whose query complexity is polynomial in 1/ . We further show that the same characterization also a...
Noga Alon, Asaf Shapira
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2003
Where STOC
Authors Noga Alon, Asaf Shapira
Comments (0)