An extension of a theorem of Fulkerson and Gross

Abstract

Fulkerson and Gross proved a theorem regarding 0–1 matrices that have the consecutive ones property. They then used it to test for this property for a given matrix. This was extended to matrices with the circular ones property by Tucker. It was further extended to the one drop property, which occurs in integer programming problems that arise in scheduling. When this result was presented, the question was raised whether there is a hierarchy of such properties and theorems. This paper answers this question in the affirmative. These results may help in testing matrices for these properties and also in solving these integer programs.