Abstract :
In this paper we show that the hamiltonian tournaments Hm, m ⩾ 4, with a normal simple quotient are reconstructible from their cards if we exclude one tournament of order 5 and two tournaments with 6 vertices. We denote by the class of such tournaments. The class of hamiltonian tournaments with a normal simple quotient contains the hamiltonian tournaments with the least number of 3-cycles (see []) and the ones that have only one hamiltonian cycle (see []). Of course, contains the class of normal tournaments with at least 4 vertices which was already considered in [].
The class has a small overlapping with the class of reconstructible simply disconnected tournaments (see []), which extends the class ℋ ℳ of reconstructible hamiltonian Moon tournaments (see []), and an empty intersection with the class ℛ of reducible tournaments with at least 5 vertices considered in []. More precisely and the classes and intersect in their tournaments with simple quotient C3.
