Decomposition and \(l_1\)-embedding of weakly median graphs (Q1582477)

The authors give a structure theory for finite weakly median graphs. They show that each such graph can be obtained by successive applications of gated amalgamations from Cartesian products of members in a short list of certain prime graphs. Furthermore they show that any such graph admits a distance-preserving embedding (\(l_1\)-embedding) into some Euclidean space. There is a scale-2-embedding into some hypercube if and only if the graph does not contain an induced subgraph \(K_{1,1,1,1,2}\).