Ordered h-hypertrees

Abstract

In this paper a special class of h-uniform hypergraphs, called μ-ordered h-hypertrees relatively to a total order μ on the vertex set is introduced. Seven other equivalent definitions of such hypertrees are proposed involving the notions of μ-ordered path and μ-ordered cycle. It is also proved that for a fixed order μ the sets of edges of μ-ordered h-hypertrees with the same vertex set is the set of bases of a graphic matroid and every h-hypertree can be recognized in polynomial time.