  In this paper we investigate k-submodular functions. This natural family of
discrete functions includes submodular and bisubmodular functions as the
special cases k = 1 and k = 2 respectively.
  In particular we generalize the known Min-Max-Theorem for submodular and
bisubmodular functions. This theorem asserts that the minimum of the
(bi)submodular function can be found by solving a maximization problem over a
(bi)submodular polyhedron. We define and investigate a k-submodular polyhedron
and prove a Min-Max-Theorem for k-submodular functions.
