Combinatorics Seminar

When: Sunday, November 19, 10am Where: Schreiber 309 Speaker: Shachar Sapir, Tel Aviv University Title: The Induced Graph Removal Lemma in Sparse Graphs

Abstract:

The induced removal lemma of Alon, Fischer, Krivelevich and Szegedy states that if an n-vertex graph G is ε-far from being induced H-free then G contains c⋅n^h induced copies of H for some c=c(ε). Improving upon the original proof, Conlon and Fox proved that 1/c is at most a tower of height poly(1/ε), and asked if this bound can be further improved to a tower of height log(1/ε). We will show how to obtain such a bound for graphs G of density O(ε). We will actually prove a more general result, which, as a special case, also gives a new proof of Fox's upper bound for the (non-induced) removal lemma.

In the second part of the talk, if time allows, we will discuss the relation between being far from (induced) H-freeness, and having many pairwise-disjoint (induced) copies of H. We will show that in the induced case, this relation can't give us the same bounds as in the non-induced case, regarding the number of pairwise-disjoint induced copies of H.

Joint work with A. Shapira.