Recognition of probe distance-hereditary graphs

Authors:
Maw-Shang Chang;Ling-Ju Hung;Peter Rossmanith
Affiliations:
Department of Computer Science and Information Engineering, HungKuang University, 43302 Sha Lu, Taichung, Taiwan;Department of Computer Science and Information Engineering, HungKuang University, 43302 Sha Lu, Taichung, Taiwan;Department of Computer Science, RWTH Aachen University, 52056 Aachen, Germany
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

Let G denote a graph class. An undirected graph G is called a probe G graph if one can make G a graph in G by adding edges between vertices in some independent set of G. By definition graph class G is a subclass of probe G 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 O(nm)-time algorithms to recognize probe distance-hereditary graphs and probe bipartite distance-hereditary graphs where n and m are the numbers of vertices and edges of the input graph respectively.