Recognition of probe distance-hereditary graphs

Abstract: Let denote a graph class. An undirected graph is called a probe graph if one can make a graph in by adding edges between vertices in some independent set of . By definition graph class is a subclass of probe graphs. 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 propose -time algorithms to recognize probe distance-hereditary graphs and probe bipartite distance-hereditary graphs where and are the numbers of vertices and edges of the input graph respectively. [Copyright &y& Elsevier]