On a certain class of nonideal clutters

In this paper we define the class of near-ideal clutters following a similar concept due to Shepherd [Near perfect matrices, Math. Programming 64 (1994) 295–323] for near-perfect graphs. We prove that near-ideal clutters give a polyhedral characterization for minimally nonideal clutters as near-perfect graphs did for minimally imperfect graphs. We… (More)