# Combinatorics Seminar

When: Sunday, June 2, 10am

Where: Schreiber 309

Speaker: Asaf Ferber, Tel Aviv University

Title: Robustness of properties of graphs and hypergraphs

## Abstract:

We discuss a few topics related to measurement of robustness of various
properties of graphs and hypergraphs. At the beginning of the talk
we discuss some properties of G(n,p) which can be preserved after a
Maker-Breaker game, i.e, a two players game played on the edge-set of a
given graph G, in which Maker's goal is to build a subgraph of G which
preserves some given property P (e.g, connectivity, Hamiltonicity etc.),
and Breaker's goal is to try to prevent Maker from doing so. At the second
part of the talk we discuss problems related to counting and packing
Hamilton cycles in dense graphs, digraphs and hypergraphs. We would like
to present a general method, based on estimating the permanent of the
adjacency matrix of a graph, for tackling these kind of problems. We then
show how to utilize this approach to prove several extremal results. At
the end of the talk, we show how to obtain similar results for dense
hypergraphs and present some challenging open problems.

All the discussed results are part of my PhD thesis under the
supervision of Prof. Michael Krivelevich, and are based on joint
works with Dennis Clemens, Roman Glebov, Dan Hefetz, Michael
Krivelevich, Anita Liebenau, Alon Naor and Benny Sudakov.

redesigned by barak soreq