A characterization of 3-Steiner distance hereditary graphs
D. P. Day, Ortrud R. Oellermann, Henda C. Swart · Networks · 1997
Let G be a connected graph and S ⊆ V(G). Then, the Steiner distance of S in G, denoted by dG(S), is the smallest number of edges in a connected subgraph of G that contains S. A connected graph G is k-Steiner distance hereditary, k ≥ 2, if for every S ⊆ V(G) such that |S| = k and every connected induced subgraph H of G containing S, dH(S) = dG(S). Some general properties about the cycle structure of k-Steiner distance hereditary graphs are established. These are then used to characterize 3-Steiner distance hereditary graphs. © 1997 John Wiley & Sons, Inc. Networks 30: 243–253, 1997