HEREDITARY HEMIMORPHY OF {-κ}-HEMIMORPHIC TOURNAMENTS FOR ≥ 5
Moncef Bouaziz, Youssef Boudabbous, Nadia El Amri · Journal of the Korean Mathematical Society · 2011
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 ${\kappa}{\geq}5$ .