A larger class of reconstructible tournaments

Abstract

In this paper we show that the hamiltonian tournaments H m , 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 [ 7]) and the ones that have only one hamiltonian cycle (see [ 19]). Of course, ▪ contains the class ▪ of normal tournaments with at least 4 vertices which was already considered in [ 8]. The class ▪ has a small overlapping with the class ▪ of reconstructible simply disconnected tournaments (see [ 19]), which extends the class ℋ ℳ of reconstructible hamiltonian Moon tournaments (see [ 12]), and an empty intersection with the class ℛ of reducible tournaments with at least 5 vertices considered in [ 13]. More precisely ▪ and the classes ▪ and ▪ intersect in their tournaments with simple quotient C 3.