On Paths of Greedoids and a Minor Characterization

Let pn denote the maximum number of paths a greedoid over n elements can have. As an upper bound, we of course have pn < 2n. We establish a lower bound for the maximum: 1.6·3n/3 < pn. In the class of simple greedoids (those greedoids on n elements having exactly n paths), we provide an excluded minor characterization of simple interval greedoids: a simple greedoid is an interval greedoid iff it has no minor isomorphic to 2(a, b, c)\{a, c}.