k-Probe DH-graphs
  Let k be a natural number. Let G be a graph and let N_1,...,N_k be k independent sets in G. The graph G is k-probe distance hereditary if G can be embedded into a DH-graph by adding edges between vertices that are contained in the same independent set. We show that there exists a polynomial-time algorithm to check if a graph G is k-probe distance hereditary. 
T. Kloks
cs.DS