# On Poset Sandwich Problems

3 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A graph $G_s=(V,E_s)$ is a sandwich for a pair of graph $G_t=(V,E_t)$ and $G=(V,E)$ if $E_t\subseteq E_s\subseteq E$. Any poset, or partially ordered set, admits a unique graph representation which is directed and transitive. In this paper we introduce the notion of sandwich poset problems inspired by former sandwich problems on comparability graphs. In particular, we are interested in series-parallel and interval posets which are subclasses of 2-dimensional posets, we describe polynomial algorithms for these two classes of poset sandwich problems and then prove that the problem of deciding the existence of a 2-dimensional sandwich poset is NP-complete.
Document type :
Conference papers
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00269577
Contributor : Christine Carvalho de Matos <>
Submitted on : Wednesday, February 6, 2019 - 12:57:18 PM
Last modification on : Wednesday, November 20, 2019 - 3:06:42 AM

### Identifiers

• HAL Id : lirmm-00269577, version 1

### Citation

Michel Habib, David Kelly, Emmanuelle Lebhar, Christophe Paul. On Poset Sandwich Problems. EuroComb: European Conference on Combinatorics, Graph Theory and Applications, 2003, Prague, Czech Republic. ⟨lirmm-00269577⟩

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