# Moncef Ben Salem Bouaziz المنصف بن سالم بوعزيز

Associate Professor

أستاذ مشارك, قسم الرياضيات بجامعة الملك سعود. أستاذ مشارك بجامعة تونس المنار

كلية العلوم
Building 4, Floor 2, Office NO: A152
publication
Journal Article
2020

# 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 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.

Publisher Name
ٍSpringer
Publishing City
USA
Volume Number
43
Magazine \ Newspaper
Bulletin of the Malaysian Mathematical Sciences Society
Pages
2297 إلى 2312
more of publication

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Abstract: Let P and P' be two orders on the same set X. The order P' is hemimorphic to P if it isomorphic to P or to its dual P*. It is hereditarily hemimorphic to P if for each subset A of X, the…

2017
Published in:
Old City Publishing

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…

2020
Published in:
ٍSpringer