A characterization of median graphs (Q762504)

A connected graph G is median graph if for any three points a, b, c there is a unique point t satisfying the equations \(d(a,b)=d(a,t)+d(t,b)\), \(d(a,c)=d(a,t)+d(t,c)\) and \(d(b,c)=d(b,t)+d(t,c)\). A pointset B is a convex if B contains all points of any shortest a-b path for every pair a,b\(\in B\). The paper gives a characterization of median graphs by means of convex sets in graphs.