Abstract
Given a class of graphs, \(\mathcal{G}\), a graph G is a probe graph of \(\mathcal{G}\) if its vertices can be partitioned into two sets, ℙ (the probes) and ℕ (the nonprobes), where ℕ is an independent set, such that G can 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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Chandler, D.B., Chang, MS., Kloks, T., Le, V.B., Peng, SL. (2008). Probe Ptolemaic Graphs. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_46
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DOI: https://doi.org/10.1007/978-3-540-69733-6_46
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