Probe Bipartite Distance-Hereditary Graphs

Abstract

A graph G = (V,E) is called a probe graph of graph class G if V can be partitioned into two sets P (probes) and N (nonprobes),where N is an independent set, such that G can be embedded into a graph of G by adding edges between certain nonprobes. A graph is distance hereditary if the distance between any two vertices remains the same in every connected induced subgraph. Bipartite distance-hereditary graphs are both bipartite and distance hereditary. In this paper we give an O(nm)-time algorithm for recognizing probe graphs of bipartite distance-hereditary graphs.