The Graph Removal Lemma

Series: 
Combinatorics Seminar
Wednesday, October 20, 2010 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Math, MIT
Organizer: 
Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(n^h) copies of H can be made H-free by removing o(n^2) edges. We give a new proof which avoids Szemeredi’s regularity lemma and gives a better bound. This approach also works to give improved bounds for the directed and multicolored analogues of the graph removal lemma. This answers questions of Alon and Gowers.