A Berge-keeping operation for graphs Original Research Article

We prove that a certain simple operation does not create odd holes or odd antiholes in a graph unless there are already some. In order to apply it, we need a vertex whose neighborhood has a coloring where the union of any two color classes is a connected graph; the operation is the shrinking of each of the color classes. Odd holes and antiholes do have such a vertex, and this property of minimal imperfect graphs implies the strong perfect graph theorem through the results of the paper. Conceivably, this property may be a target in the search for a proof of the strong perfect graph theorem different from the monumental achievement of Chudnovsky, Robertson, Seymour, and Thomas.