  We present various new results on greedoids. We prove a theorem that
generalizes an equivalent formulation of Edmonds' classic matroid polytope
theorem to local forest greedoids -- a class of greedoids that contains
matroids as well as branching greedoids. We also describe an application of
this theorem in the field of measuring the reliability of networks by
game-theoretical tools. Finally, we prove new results on the optimality of the
greedy algorithm on greedoids and correct some mistakes that have been present
in the literature for almost three decades.
