Finite Orders Which Are Reconstructible up to Duality by Their Comparability Graphs

A finite order P on a set V is reconstructible (respectively, reconstructible up to duality) by its comparability graph if each order on V which has the same comparability graph as P is isomorphic to P (respectively, is isomorphic to P or to its dual P ⋆ ). In this paper, we describe the finite orde...

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Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 43; no. 3; pp. 2297 - 2312
Main Authors Alzohairi, Mohammad, Bouaziz, Moncef, Boudabbous, Youssef, Sharary, Ahmad
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.05.2020
Springer Nature B.V
Subjects
Applications of Mathematics
Graphs
Mathematics
Mathematics and Statistics
Reconstruction
05C20
Comparability graph
Ordered set
05C60
Modular decomposition
Isomorphism up to duality
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Summary:A finite order P on a set V is reconstructible (respectively, reconstructible up to duality) by its comparability graph if each order on V which has the same comparability graph as P is isomorphic to P (respectively, is isomorphic to P or to its dual P ⋆ ). In this paper, we describe the finite orders which are reconstructible up to duality by their comparability graphs. This result is motivated by the characterization, obtained by Gallai (Acta Math Acad Sci Hungar 18:25–66, 1967 ), of the pairs of finite orders having the same comparability graph. Notice that a characterization of the finite orders which are reconstructible by their comparability graphs is easily deduced from Gallai’s result.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-019-00805-w