A Note on Minimal Senders

Abstract

In this paper we prove that if a pair of graphs G,H have senders, then they necessarily have connected minimal senders; we also prove that given two fixed graphs that are either 3-connected or triangles there are minimal (G,H)-senders with arbitrarily distant signal edges and (G,H)-minimal graphs with arbitrarily large cycles, thus showing there is no upper bound for the diameters of (G,H)-minimal graphs.