On compact median graphs
Claude Tardif · Journal of Graph Theory · 1996
A median graph is called compact if it does not contain an isometric ray. This property is shown to be equivalent to the finite intersection property for convex sets. We show that a compact median graph contains a finite cube that is fixed by all of its automorphisms, and that each family of commuting endomorphisms of a compact median graph fixes a common cube. © 1996 John Wiley & Sons, Inc.