In Search of Hyperpaths

Hypertrees are high-dimensional counterparts of graph theoretic trees. They have attracted a great deal of attention by various investigators. Here we introduce and study hyperpaths —a particular class of hypertrees which are high dimensional analogs of paths in graph theory. A d -dimensional hyperpath is a d -dimensional hypertree in which every (d-1) -dimensional face is contained in at most (d+1) faces of dimension d . We introduce a possibly infinite family of hyperpaths for every dimension, and investigate its properties in greater depth for dimension d=2 .