Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2010.02.10
  • Published : 2011.05.01
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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 ${\kappa}{\geq}5$.

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