# 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
2017

# Description of the Orders Which are Hereditarily Half-reconstructible by Their Comparability Graphs

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 orders P↿A and P'↿A induced on A are hemimorphic. The order P is hereditarily half-reconstructible by its comparability graph if it is hereditarily hemimorphic to each order Q on X having the same comparability graph as P. In this paper, we begin by obtaining a new result on the decomposition of orders. Then we use this result to describe the orders which are hereditarily half-reconstructible by their comparability graphs. By the last result we solve an open problem posed in 2013, by Alzohairi, Bouaziz, and Boudabbous.

Publisher Name
Old City Publishing
Publishing City
USA
Volume Number
29
Issue Number
3-4
Magazine \ Newspaper
مجلة
Pages
373 إلى 388
more of publication

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2015
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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