Recognition of probe ptolemaic graphs

Authors:
Maw-Shang Chang;Ling-Ju Hung
Affiliations:
Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan
Venue:
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Year:
2010

Citing 11
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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. Ptolemaic graphs are chordal and induced gem free. They form a subclass of both chordal graphs and distancehereditary graphs. Many problems NP-hard on chordal graphs can be solved in polynomial time on ptolemaic graphs. We proposed an O(nm)- time algorithm to recognize probe ptolemaic graphs where n and m are the numbers of vertices and edges of the input graph respectively.