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Journal Articles Order Year : 2023

On dually-CPT and strong-CPT posets

Abstract

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 Alcón, Gudiño and Gutierrez [1] introduced proper subclasses of CPT posets, namely dually-CPT, and strongly-CPT. A poset P is dually-CPT, if and only if P and its dual P d both admit a CPT representation. A poset P is strongly-CPT, if and only 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 [1] whether strongly-CPT was a strict subclass of dually-CPT. We provide a proof that both classes actually coincide.
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Dates and versions

hal-04216376 , version 1 (24-09-2023)

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Liliana Alcón, Martin Charles Golumbic, Noemí Gudiño, Marisa Gutierrez, Vincent Limouzy. On dually-CPT and strong-CPT posets. Order, 2023, ⟨10.1007/s11083-023-09656-4⟩. ⟨hal-04216376⟩
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