| Abstract: | This paper deals with the problematic aspect of the reconstruction of binary relations: it includes all the questions raising the possibility or impossibility to determine a structure by gathering given substructures. It is the continuation of three studies: the first made by G. Lopez [9] in 1972 about the determination of a binary relation through the types of isomorphism of its restrictions, the second made by K. B. Reid and C. Thomassen [15] in 1976 about the strongly self-complementary tournaments (every subtournament is self-complementary), the third made by C. Thomassen [16] in 1989 about the cycle space of a tournament. In the second section, we use the notion of class of difference (which was introduced in [9]) to extend a study made in [16] to binary relations. Then, in the third section, we improve the result of this last study in the case of the tournaments. After noticing that the result of [15] inferred itself naturally from the approach developed in [9], we extend, in the fourth section, the study made in [15] to binary relations. |
