Mengerian quasi-graphical families and clutters

Balanceable clutters are clutters whose bipartite representation contains no odd wheel and no odd 3-path configuration as an induced subgraph (this is Truemper’s characterization of balanceable matrices). In this paper we study a proper subclass of balanceable clutters called quasi-graphical defined by forbidding one-sided even wheels and one-sided even 3-path configurations. We characterize Mengerian quasi-graphical clutters and, as a consequence, we show that a recent conjecture in Cornuéjols et al. (2000) [7] is true for quasi-graphical clutters.