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

Author

Listed:
  • Tiziana Calamoneri

    (Sapienza University of Rome)

  • Angelo Monti

    (Sapienza University of Rome)

  • Blerina Sinaimeri

    (Luiss University)

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.

Suggested Citation

  • Tiziana Calamoneri & Angelo Monti & Blerina Sinaimeri, 2025. "On Variants of PCGs: A Survey of Current Results and Open Problems," Springer Optimization and Its Applications,, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-91357-0_3
    DOI: 10.1007/978-3-031-91357-0_3
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