Probe Ptolemaic Graphs

Authors:
David B. Chandler;Maw-Shang Chang;Ton Kloks;Van Bang Le;Sheng-Lung Peng
Affiliations:
Department of Mathematical Sciences, University of Delaware Newark, Delaware, USA 19716;Department of Computer Science and Information Engineering, National Chung Cheng University, Chiayi, Taiwan 62107;Department of Mathematical Sciences, University of Delaware Newark, Delaware, USA 19716;Institut für Informatik, Universität Rostock, Rostock, Germany 18051;Department of Computer Science and Information Engineering, National Dong Hwa University, Hualien, Taiwan 97401
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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Abstract

Given a class of graphs, $\mathcal{G}$, a graph Gis a probe graph of$\mathcal{G}$ if its vertices can be partitioned into two sets, 茂戮驴 (the probes) and 茂戮驴 (the nonprobes), where 茂戮驴 is an independent set, such that Gcan be embedded into a graph of $\mathcal{G}$ by adding edges between certain nonprobes. In this paper we study the probe graphs of ptolemaic graphs when the partition of vertices is unknown. We present some characterizations of probe ptolemaic graphs and show that there exists a polynomial-time recognition algorithm for probe ptolemaic graphs.