Higher-dimensional tree structures

AbstractVarious generalizations of tree-characterization theorems are developed for n-dimensional complexes. In particular, generalizations of three conditions satisfied by trees T are studied: T is connected, T is acyclic, |V(T)| − |E(T)| = 1, where V(T) and E(T) denote the vertex and edge sets of T, respectively.Earlier work by Beineke and Pippert is extended in generalizing these conditions and studying which combinations of such conditions yield characterizations of the n-dimensional trees treated here