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http://dx.doi.org/10.4134/JKMS.2011.48.3.599

HEREDITARY HEMIMORPHY OF {-κ}-HEMIMORPHIC TOURNAMENTS FOR ≥ 5  

Bouaziz, Moncef (Department of Mathematics College of Sciences King Saud University)
Boudabbous, Youssef (Department of Mathematics College of Sciences King Saud University)
Amri, Nadia El (Departement de Mathematiques Faculte des Sciences de Monastir Universite de Monastir)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.3, 2011 , pp. 599-626 More about this Journal
Abstract
Let T = (V,A) be a tournament. With every subset X of V is associated the subtournament T[X] = (X, A ${\cap}$ (X${\times}$X)) of T, induced by X. The dual of T, denoted by $T^*$, is the tournament obtained from T by reversing all its arcs. Given a tournament T' = (V,A') and a non-negative integer ${\kappa}$, T and T' are {$-{\kappa}$}-hemimorphic provided that for all X ${\subset}$ V, with ${\mid}X{\mid}$ = ${\kappa}$, T[V-X] and T'[V-X] or $T^*$[V-X] and T'[V-X] are isomorphic. The tournaments T and T' are said to be hereditarily hemimorphic if for all subset X of V, the subtournaments T[X] and T'[X] are hemimorphic. The purpose of this paper is to establish the hereditary hemimorphy of the {$-{\kappa}$}-hemimorphic tournaments on at least k + 7 vertices, for every ${\kappa}{\geq}5$.
Keywords
tournament; isomorphy; hereditary isomorphy; hemimorphy; hereditary hemimorphy;
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