Princeton University, Princeton, NJ, USA

This is joint work with Felix Brandt, Gaku Liu, Maria Chudnovsky, Sergey Norin, Alex Scott, Paul Seymour, and Stephan Thomassé.

Seminar series on discrete mathematics @ Dept. of Mathematical Sciences, KAIST.

A counterexample to a conjecture of Schwartz

Ilhee Kim (김일희)

Princeton University, Princeton, NJ, USA

Princeton University, Princeton, NJ, USA

2012/01/11 Wed 4PM-5PM

In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that there is no tournament with a partition A, B of its vertex set, such that every transitive subset of A is in the out-neighbour set of some vertex in B, and vice versa. But in fact there is such a tournament and so Schwartz’ conjecture is false. Our proof is non-constructive and uses the probabilistic method.

This is joint work with Felix Brandt, Gaku Liu, Maria Chudnovsky, Sergey Norin, Alex Scott, Paul Seymour, and Stephan Thomassé.

This is joint work with Felix Brandt, Gaku Liu, Maria Chudnovsky, Sergey Norin, Alex Scott, Paul Seymour, and Stephan Thomassé.

Forbidden induced subgraphs of double-split graphs

Ilhee Kim (김일희)

Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA

Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey, USA

2011/1/7 Fri 4PM-5PM

In the course of proving the strong perfect graph theorem, Chudnovsky, Robertson, Seymour, and Thomas showed that every perfect graph either belongs to one of five basic classes or admits one of several decompositions. Four of the basic classes are closed under taking induced subgraphs (and have known forbidden subgraph characterizations), while the fifth one, consisting of double-split graphs, is not. A graph is doubled if it is an induced subgraph of a double-split graph. We find the forbidden induced subgraph characterization of doubled graphs; it contains 44 graphs.

This is joint work with Boris Alexeev, and Alexandra Fradkin.