On Dually-CPT and Strongly-CPT Posets

Liliana Alcón, Martin Charles Golumbic, Noemí Gudiño, Marisa Gutierrez, Vincent Limouzy

Research output: Contribution to journalArticlepeer-review


A poset is a containment of paths in a tree (CPT) if it admits a representation by containment where each element of the poset is represented by a path in a tree and two elements are comparable in the poset if the corresponding paths are related by the inclusion relation. Recently Alcón, Gudiño and Gutierrez (Discrete Applied Math. 245, 139–147, 2018) introduced proper subclasses of CPT posets, namely dually-CPT, and strongly-CPT (or strong-CPT). A poset P is dually-CPT, if P and its dual Pd both admit a CPT-representation. A poset P is strongly-CPT, if P and all the posets that share the same underlying comparability graph admit a CPT-representation. Where as the inclusion between dually-CPT and CPT was known to be strict. It was raised as an open question by Alcón, Gudiño and Gutierrez (Discrete Applied Math. 245, 139–147, 2018) whether strongly-CPT was a strict subclass of dually-CPT. We provide a proof that both classes actually coincide.

Original languageEnglish
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.


  • CPT
  • Dually-CPT
  • Poset
  • Strong-CPT

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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