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, i¾? (the probes) and i¾? (the nonprobes), where i¾? 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.
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