Abstract
Let \(\mathcal{G}\) denote a graph class. An undirected graph G is called a probe \(\mathcal{G}\) graph if one can make G a graph in \(\mathcal{G}\) by adding edges between vertices in some independent set of G. By definition graph class \(\mathcal{G}\) is a subclass of probe \(\mathcal{G}\) graphs. Ptolemaic graphs are chordal and induced gem free. They form a subclass of both chordal graphs and distance-hereditary 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.
This research is supported by National Science Council of Taiwan under grant no. NSCÂ 95-2221-E-194-038-MY3.
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Chang, MS., Hung, LJ. (2011). Recognition of Probe Ptolemaic Graphs. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2010. Lecture Notes in Computer Science, vol 6460. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19222-7_29
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DOI: https://doi.org/10.1007/978-3-642-19222-7_29
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