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Conference Papers Year : 2003

## On Poset Sandwich Problems

Michel Habib
David Kelly
• Function : Author
Emmanuelle Lebhar
• Function : Author
• PersonId : 832411
Christophe Paul

#### 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.

#### Domains

Computer Science [cs]

### Dates and versions

lirmm-00269577 , version 1 (06-02-2019)

### Identifiers

• HAL Id : lirmm-00269577 , version 1

### Cite

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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