NeST graphs Original Research Article

We establish results on NeST graphs (intersection tolerance graphs of neighborhood subtrees of a tree) and several subclasses. In particular, we show the equivalence of proper NeST graphs and unit NeST graphs, the equivalence of fixed distance NeST graphs and threshold tolerance graphs, and the proper containment of NeST graphs in weakly chordal graphs. The latter two results answer questions of Monma, Reed and Trotter, and Bibelnieks and Dearing.