On dually-CPT and strong-CPT posets

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

Research output: Working paperPreprint


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 and only if the corresponding paths are related by the inclusion relation. Recently Alc\'on, Gudi\~{n}o and Gutierrez introduced proper subclasses of CPT posets, namely dually-CPT, and strongly-CPT. A poset $\mathbf{P}$ is dually-CPT, if and only if $\mathbf{P}$ and its dual $\mathbf{P}^{d}$ both admit a CPT representation. A poset $\mathbf{P}$ is strongly-CPT, if and only if $\mathbf{P}$ 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 Alc\'on, Gudi\~{n}o and Gutierrez whether strongly-CPT was a strict subclass of dually-CPT. We provide a proof that both classes actually coincide.
Original languageEnglish
StatePublished - 10 Apr 2022

Publication series



  • cs.DM


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