Modular and median signpost systems and their underlying graphs
Henry Martyn Mulder, Ladislav Nebeský · Discussiones Mathematicae Graph Theory · 2003
The concept of a signpost system on a set is introduced. It is a ternary relation on the set satisfying three fairly natural axioms. Its underlying graph is introduced. When the underlying graph is discon-nected some unexpected things may happen. The main focus are sign-post systems satisfying some extra axioms. Their underlying graphs have lots of structure: the components are modular graphs or median graphs. Yet another axiom guarantees that the underlying graph is also connected. The main results of this paper concern if-and-only-if characterizations involving signpost systems satisfying additional ax-ioms on the one hand and modular, respectively median graphs on the other hand.