Forbidden induced subgraphs of double-split graphs
Forbidden induced subgraphs of double-split graphsIn 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.
Boris Alexeev, Alexandra Fradkin, and Ilhee Kim
Forbidden induced subgraphs of double-split graphs
SIAM Journal on Discrete Mathematics 26 (2012), no. 1, 1–14
