On a class of balanced hypergraphs

Abstract

Let P be an arborescence, and let F u = { U 1 U k }, F 1 = { V 1 V x be two systems consisting of directed subpaths of P. Minimax theorems and algorithms are proved concerning the so called bi-path system ( P; F uF x ). 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.