MVLSC HomeIssue Contents

Description of the k-hypomorphic Tournaments
Mouna Achour, Youssef Boudabbous and Abderrahim Boussaïri

Consider two tournaments T and T’ on the same vertex set V, with | V |= n ≥ 2 and let k be a positive integer. The tournaments T and T’ are {−k}-hypomorphic (resp. k-hypomorphic), whenever for every subset X of V with | X |= n − k (resp. | X |= k), the subtournaments T [X] and T [X] are isomorphic. The tournament T is {−k}-self dual (resp. k-self dual) if it is {−k}-hypomorphic (resp. k-hypomorphic) to its dual. In this work, we firstly characterize the pairs of {−3}- hypomorphic tournaments, following our previous study of “the {−3}- reconstruction and the {−3}-self duality of tournaments”, and then we characterize the pairs of k-hypomorphic tournaments for k ≥ 1.

Keywords: Tournament, tournament without diamonds, hypomorphy, self duality, modular partition.

Full Text (IP)