Split Decomposition and Distance Labelling: An Optimal Scheme For Distance Hereditary Graphs

Distance hereditary graphs are those graphs for which in any connected induced subgraph, the distance between any two vertices in this subgraph is equal to their distance in the whole graph. This class strictly contains trees. We show how the distance labelling scheme for trees presented in [?] can be extended to distance hereditary graphs with optimal length labels. The result is based on the split decomposition of a graph [?].