Prime 2-structures

Pierre Ille (1)

1 I2M - Institut de Mathématiques de Marseille

The 2-structures generalize arc-coloured digraphs. They are obtained from a vertex set by considering an equivalence relation between the ordered pairs of distinct vertices. The 2-structures provide a suitable framework to introduce the modular decomposition. A vertex subset of a 2-structure is a module whenever each vertex outside is linked in an equivalent way to all the vertices inside. A 2-structure is prime if it does not admit proper modules with at least 2 elements. Our purpose is to study the possible cardinalities of the prime 2-substructures in a finite or infinite prime 2-structure.

Keywords: 2-structure; module; prime

Domains: Mathematics [math]

Pierre Ille. Prime 2-structures. 19 (1), 2024, ⟨10.55016/ojs/cdm.v19i1⟩. ⟨hal-04570639⟩