On Variants of PCGs: A Survey of Current Results and Open Problems

Tiziana Calamoneri (), Angelo Monti () and Blerina Sinaimeri ()
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Tiziana Calamoneri: Sapienza University of Rome
Angelo Monti: Sapienza University of Rome
Blerina Sinaimeri: Luiss University

A chapter in Theory, Algorithms, and Experiments in Applied Optimization, 2025, pp 39-59 from Springer

Abstract: Abstract A graph is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tree where each leaf corresponds to a vertex of the graph, and an edge u , v $${u,v}$$ exists in the graph if and only if the weight of the path connecting the leaves u and v in the tree falls within a specified interval. PCGs have been extensively studied, and numerous subclasses and generalizations have been introduced, expanding their applicability and theoretical interest. In this survey, we briefly review the existing results on these variants of PCGs and highlight several intriguing open problems, focusing on the main challenges and potential directions for future research.

Date: 2025
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DOI: 10.1007/978-3-031-91357-0_3

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