## Combinatorics Seminar

When: Sunday, October 26, 10am
Where: Schreiber 309
Speaker: Raphy Yuster, University of Haifa
Title: Unavoidable tournaments
## Abstract:

A basic result in Ramsey theory states that any tournament
contains
a "large" transitive subgraph. Since transitive tournaments
contain
only transitive subgraphs, it is natural to ask which subgraphs
must appear in any large tournament that is "far" from being
transitive. One result of this type was obtained by Fox and
Sudakov,
who characterized the tournaments that appear in any tournament
that
is epsilon-far from being transitive. Another result of this type
was obtained by Berger et al., who characterized the tournaments
that
appear in any tournament that cannot be partitioned into a bounded
number of transitive sets.
In this talk we consider the common generalization of the above
two
results, namely the tournaments that must appear in any tournament
that is epsilon-far from being the union of a bounded number of
transitive sets. Our main result is a precise characterization of
these tournaments.
Joint work with A. Shapira.