Let P be an arborescence, and let Fu = {U1Uk}, F1 = {V1Vx be two systems consisting of directed subpaths of P. Minimax theorems and algorithms are proved concerning the so called bi-path system (P; FuFx). One can define a hypergraph to every bi-path system. The class of these “bi-path” hypergraphs is closed under forming of dual, sub and partial hypergraph. Every bi-path hypergraph is balanced but not necessarily unimodular.
