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.